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Even numbers : they can be written 2n

2n1+2n2+....+2nm = 2(n1+n2+....+nm) so it's always an even number

2n1x 2n2x....x2nm = 2(n1+n2+....+nm) which is always an even number

Odd numbers: they canbe written 2n+1

(2n1+1) + (2n2+1) + ....+ (2nm +1) = 2(n1+n2+....+nm) + m which is even if m is even and odd if m is odd, so it depend of the number of terms

(2n1+1) x (2n2+1) x ....x (2nm +1) is always odd cause the last term of the expansion is always +1 and other terms have at least 2 as factor

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Q: What do you know about the sums and the product of odd and even numbers?
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