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Number Theory Course , I need a full explained answer for those proofs please 1. Prove...

Number Theory Course , I need a full explained answer for those proofs please

1. Prove that for every integer x, x + 4 is odd if and only if x + 7 is even.
2. Prove that for every integer x, if x is odd then there exists an integer y such that x^2 = 8y + 1.

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