Find the smallest positive interger x such that 1001 x leaves a remainder of 70 when divided by 315

Q: Determine whether there are infinitely many primes that have a remainder of 12 when divided by 25.…

A: Given question is Determine whether there are infinitely many primes that have a remainder of 12…

Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

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Q: Find the greatest natural number n such that n + 10 divides nº + 100.

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Q: A number that has exactly 2 factors (1 and itself) is called a number. * O factors O prime O…

A: We have asked if a number that has exactly 2 factors (1 and itself) then what kind of number is…

Q: 86- The remainder upon the division of x 98 + 4 by x – 4 in Z, is:

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Q: Find P(Z < 2.84)     .5375     .9575     .8098     .9977

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Q: What is the smallest positive integer n such that 80325 divides n!

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Q: 1. Find the greatest number which divides 64 and 80 completely. 2. Find the least number which when…

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Q: If 6th term of a G.P. is 9375 and its 4th term is 375.Find its 9th term.

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Q: 1) A large cube is made up of 2 by 2 by 2 cubes. Find the total number of 1 x 1 x1 cubes in this…

A: Volume of Cube = a3

Q: Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2…

A: Let N be such a number N=10a+9:  N+1 = 10a+10 N=9b+8: N+1 = 9b+9 N=8c+7: N+1 = 8c+8 N=7d+6 and so on…

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: When we multiply 37 Sect ion X 26 by using the standard multiplication algorithm, we start the…

A: Multiplication can be thought of as repeated addition. So, if you multiply a number a by another…

Q: Find all integer partitions of 10.

A: A Partition of a positive number n or integer partition is a way of calculating all  n sum of…

Q: You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your…

A: We will find a sequence for number of bacteria .

Q: Show that if 5 divides n2 with remainder 4, 5 divides 3n3 with remainder 2.

A: Given that 5 divides n2 5 n25 n×n5 n5 n3 As it gives the remainder 4 on dividing by 5. Therefore it…

Q: Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the…

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Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: Find P(−1.5465 > z > 1.1143).

A: For a continuous random variable X, with mean μ and standard deviation σ, P(α&lt;X&lt;β) =…

Q: When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by 7? Moreover,…

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Q: 1. Find the sum of the first 50 even positive integers.

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Q: Find the proportion of primes p in the interval from 10^12 and 10^12 + 1000 such that p-1 is B= 105…

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Q: 6. Find x in ADEF.

A: We have the given figure as We have to find the value of x

Q: 1. If the 2nd term of a GPis 108 and the 5th term is 256, find the common ratio and the first term.

A: Given 2nd term of GP is 108 and the 5th term is 256

Q: Find a rational fraction equivalent to following infinitely repeating decimal: a.)3.123123 b)…

A: a.let x=3.123123............(i)multiply by 10001000x=3123.123123...........(ii)substract…

Q: of all rabbits in a country are in one state and - of the rabbits are in a different state, what…

A: We have that 5/32 of all rabbits in a country are in one state and 2/7 of the rabbits are in a…

Q: 1. Find the remainder when 53751 is divided by 11.

A: 1. We will use the Euler's theorem, to find the remainder.

Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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Q: Use Fermat’s and/or Euler’s Theorem. Find the remainder of 72021 when divided by 8

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Q: Find the largest number 8 such that 1 if 0 < r – 0.9| < S then <1.6. 0.92 8 =

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in.…

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Q: Find the minimal integer number that: Gives remainder 1 on division by 3 Gives remainder 2 on…

A: We have to use Chinese remainder theorem in this question.

Q: Find the largest negative integer leaves a remainder 2 when divided by 3, 5, and 12. (If it is not…

A: Let us  solve the question in the next step.

Q: 6. Find the remainder when 721 divided by 43 7. For a given integer n, prove that 3 k-0

A: To find the remainder when 7221 divided by 43. Now, 7 and 43 are relatively prime and 43 is a prime…

Q: Suppose that one selects some subset of integers from the set {1, 2, ., 47). What is the smallest…

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Q: "For all integers n, n(n² – 1) is divisible by 6." (You may use quotient-remainder theorem and…

A: Let us consider, for all integers n a = n3 – n a = n (n2 – 1) a = n (n + 1)(n – 1)

Q: Use the quotient remainder theorem and division into cases to show for all integers n, the integer…

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Q: to binary. II. Show that any weight not exceeding 2 - 1 may be measured using weights of 1, 2,…

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Q: Find the least positive remainder and quotient of -123455781 when divided by 911.

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Q: If the 2nd, 3rd  and 4th term in a GP are 12, 36 and 108   What is the 1st term and the common ratio

A: It is given that, the 2nd, 3rd and 4th term in a GP is 12, 36 and 108.

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: By Binomial expansion, we know that the pth term of the expansion x+yn is np-1 xp-1yn+1-p. So we get…

Q: Find the sum of all integers from 41 to 83. The sum of all integers from 41 to 83 is

A: Detailed Solution and Explanation is given below....

Q: Use Fermat's and/or Euler's Theorem to answer the following Find the remainder of 74 when divided by…

A: We have to n find the remainder of 74 when divided by 8 using fermat's little theorem or Euler's…

Q: Prove that C(n + 4, r + 1) = C(n + 3, r + 1) + C(n + 3, r). Hint: expand each Combination and use…

A: Explanation of the answer is as follows

Q: Suppose n is odd. Find the cube of n and divide it by 4. What possible remainders could occur? Check…

A: Solution

Q: find the nth term of 1/5, 1/10, 1/15, ... , n = 10

A: In this question we have to find the nth term where n is 10.

Q: If 6th term of a G.P is 9375 and its 4th term is 375.Find its 9th term

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Q: Find the smallest positive integer N that satisifies all of the following conditions N is a square…

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Q: Show that 19 divides 10*8n-1 + 33n-1 for every positive integer n.

A: Concept: Mathematical induction: For each and every natural number n, mathematical induction is a…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.