21. Let p be an odd prime and let n be a positive integer. Use the...

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21. Let p be an odd prime and let n be a positive integer. Use the Binomial Theorem to show = 1(mod p") but (1 + p)p"-2 # 1 (mod p"). Deduce that 1 + p is an element of order pn-1 in the multiplicative group (Z/p"Z)*. that (1 + p) 21. Let p be an odd prime and let n be a positive integer. Use the Binomial Theorem to show = 1(mod p") but (1 + p)p"-2 # 1 (mod p"). Deduce that 1 + p is an element of order pn-1 in the multiplicative group (Z/p"Z)*. that (1 + p)

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The Binomial Theorem states that for any integer n a bn Cn 0an b0 Cn 1an1 b1 Cn n1a1 bn1 Cn na0 bn w... View the full answer