Given the set M = {x | x = A & # 178; - B & # 178;, a, B ∈ Z}, we prove that if K ∈ Z, then 2K + 1 ∈ M

Given the set M = {x | x = A & # 178; - B & # 178;, a, B ∈ Z}, we prove that if K ∈ Z, then 2K + 1 ∈ M

M={x|x=a²-b²,a,b∈Z}
k∈Z
Let B = k, a = K + 1
Then x = A & # 178; - B & # 178; = (K + 1) &# 178; - K & # 178; = 2K + 1
So obviously 2K + 1 ∈ M
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