• # question_answer If ${{P}_{1}}$ and ${{P}_{2}}$ are two odd primes numbers such that ${{P}_{1}}>{{P}_{2}}$then $P_{1}^{2}-P_{2}^{2}$ is A)  an Even numberB)  an odd numberC)  an odd prime number            D)  a prime number

${{P}_{1}}^{2}-{{P}_{2}}^{2}=:\left( \underset{\begin{smallmatrix} \downarrow - \\ odd \end{smallmatrix}}{\mathop{{{p}_{1}}}}\,-\underset{odd}{\mathop{\underset{\downarrow }{\mathop{{{p}_{2}}}}\,}}\, \right)\left( \underset{\begin{smallmatrix} \downarrow \\ odd \end{smallmatrix}}{\mathop{{{p}_{1}}}}\,+\underset{odd}{\mathop{\underset{-\downarrow }{\mathop{{{p}_{2}}}}\,}}\, \right)$ ($\because$odd - odd = Evan) $(5-3=2)$ $Even\times Even=Even$