Prove that 3k+2 is not perfect square for all k∈{0,1,2,3,...}.


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Question Number 23269 by Rasheed.Sindhi last updated on 28/Oct/17

$P rove that$ $3 k + 2 is not perfect square for$ $all k \in {0, 1, 2, 3, . . .} .$
	Answered by Tinkutara last updated on 28/Oct/17

	$A n y n u m b e r c a n b e w r i t t e n a s 3 p,$ $3 p + 1 a n d 3 p + 2 .$ $I f i t i s 3 p, {i t}^{'} s s q u a r e = 9 p^{2} = 3 k f o r m$ $I f i t i s 3 p + 1, {i t}^{'} s s q u a r e = 9 p^{2} + 6 p + 1$ $= 3 k + 1 f o r m$ $I f i t i s 3 p + 2, {i t}^{'} s s q u a r e = 9 p^{2} + 12 p + 4$ $= 3 k + 1 f o r m$ $H e n c e a s q u a r e c a n n o t b e i n 3 k + 2$ $f o r m .$
	Commented by Rasheed.Sindhi last updated on 28/Oct/17

	$T han X a lot sir!$
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