Please Be Clear With Your Proofs Use Complete Sentences If Possible 1 (47.48 KiB) Viewed 27 times
Please be clear with your proofs, use complete sentences ifpossible.
Bézout's identity: Let a,b∈Z with gcd(a,b)=1. Then there exists x,y∈Z such that ax+by=1. (For example, letting a=5 and b=7 we can use x=10 and y=−7) Using Bézout's identity, show that for a∈Z and p prime, if a≡0(modp) then ak≡1 (modp) for some k∈Z
0 . Prove that if n∈Z is even, then either n=4k or n=4k+2 for some integer k. You may assume that every integer is either even or odd. (Food for thought: try to prove this fact.)
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