forall k,l inZ,kl is even⟹k is even vee l is even. Suppose k is odd and l is odd, then there exist integers a and b such that k=2a+1, so kl=(ab??)

Stephanie Hunter

Stephanie Hunter

Answered question

2022-07-19

k , l Z , k l  is even k  is even  l  is even .
Suppose k is odd and l is odd, then there exist integers a and b such that k = 2 a + 1, so k l = ( a b ? ? )

Answer & Explanation

Vartavk

Vartavk

Beginner2022-07-20Added 11 answers

For an indirect proof, we assume the opposite to be true and find a contradiction. This means we assume
k , l Z : ( 2 k l 2 k , l )
Notice that then k = 2 a + 1 and l = 2 b + 1, therefore k l = ( 2 a + 1 ) ( 2 b + 1 ) = 2 ( 2 a b + a + b ) + 1 which clearly contradicts the assumption 2 k l

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