Question

If p is a positive integer, which could be an odd integer?

Answer 1

$p > 0 \Rightarrow$

$2p+2$ (even)

$p^3-p$ (odd or even)

$p^2 + p$ (even)

$p^2 - p$ (even)

$7p - 3$ (ODD); 7p odd, 7p-3 = (odd)-(odd)=(odd)

Answer 2

$p>0\\\\(A)\ \ \ 2p+2=2(p+1)\ \rightarrow\ \ even\ number\\\\(B)\ \ \ p^3-p=p(p^2-1)=p(p-1)(p+1)\ \rightarrow\ \ even\ number\\\\(C)\ \ \ p^2+p=p(p+1)\ \rightarrow\ \ even\ number\\\\(D)\ \ \ p^2-p=p(p-1)\ \rightarrow\ \ even\ number\\\\(E)\ \ \ 7p-3=6p-4+p+1=2(3p-2)+p+1\\\\p-odd\ \rightarrow\ \ (p+1)- even\ \rightarrow\ (7p-3)-even\ number\\\\p-even\ \rightarrow\ \ (p+1)- odd\ \rightarrow\ (7p-3)-odd\ number\\\\Ans.\ E$