Mathematics, 18.02.2020 22:54 chrissak8118
Let n be a positive odd integer. Prove that n4 ≡ 1 (mod 16). You may use any of the mod rules provided in class (In addition, if you end up getting an expression of the form a (3a+1) somewhere in your work where a is an integer, separately end up proving that this expression is always even and use that result to complete your proof).
Answers: 2
is odd, then we can write 
for some 
.
is 8 times the product of two consecutive integers, one even and the other odd. This product is even and thus divisible by 2, so that 
where 
, and the equivalence further reduces to
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Let n be a positive odd integer. Prove that n4 ≡ 1 (mod 16). You may use any of the mod rules provid...
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