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gmer
Group Title
Prove that if n is an integer, then n^2 mod 5 is either 0,1, or 4
 one year ago
 one year ago
gmer Group Title
Prove that if n is an integer, then n^2 mod 5 is either 0,1, or 4
 one year ago
 one year ago

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Shadowys Group TitleBest ResponseYou've already chosen the best response.1
there are only five possible ways for n. first case: \(n \equiv 0(mod 5)\), then \(n^2 \equiv 0(mod 5)\) second case: \(n \equiv 1(mod 5)\)), then \(n^2 \equiv 1(mod 5)\) third case:\(n \equiv 2(mod 5)\)), then \(n^2 \equiv 4(mod 5)\) fourth case:\(n \equiv 3(mod 5)\)), then \(n^2 \equiv 6(mod 5)\), which is equal to \(n^2 \equiv 1(mod 5)\), as \(6 \equiv 1(mod 5)\) fifth case:\(n \equiv 4(mod 5)\)), then \(n^2 \equiv 16(mod 5)\) which is equal to \(n^2 \equiv 1(mod 5)\), as \(16 \equiv 1(mod 5)\) so we conclude that if n is an integer, n^2 mod 5 is either 0,1, or 4
 one year ago

Shadowys Group TitleBest ResponseYou've already chosen the best response.1
sorry, for fourth case, it's \(n^2 \equiv 9 (mod 5)\) and it's equal to \(n^2 \equiv 4 (mod 5)\)
 one year ago

gmer Group TitleBest ResponseYou've already chosen the best response.0
Excellent, but how do we know that there are only five possible values for n?
 one year ago

Shadowys Group TitleBest ResponseYou've already chosen the best response.1
because the remainder for any integer k divided by an integer n has only n1 remainders. e.g. for 2, you can only get 0 or 1 as remainder. any other remainder means that the division is incomplete.
 one year ago

Shadowys Group TitleBest ResponseYou've already chosen the best response.1
sorry it'snot n1, it's n. but the range is 0,1,2,3,...,n1
 one year ago
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