(10) Prove that for any prime number P>3. p² = 1 (mod 24) (Hint: chinese remainder theorem tells us need to show SP² = 1 (mod 3) 2p² = 1 (mod 8) we only The hard part is to show p² = 1 (mod 8), which means 81 p2-1 = P (P-1) (P+) we know that must be odd. Hence, P two integers. P+1 are " So it is enough to show 21욎. 왤).

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