if p2 is an even integer , prove that p is an even integer

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Solution

Dear Student,

$W e a r e g i v e n t h a t p^{2} i s a n e v e n i n t e g e r i . e . i t' s u n i t p l a c e h a s 0, 2, 4, 6 o r 8 A t u n i t p l a c e w e c a n h a v e o n l y 10 o p t i o n s i . e . 0 - 9 0^{2} = 0 1^{2} = 1 2^{2} = 2 3^{2} = 9 4^{2} = 6 5^{5} = 5 6^{2} = 6 7^{2} = 9 8^{2} = 4 9^{2} = 1 T h e r e f o r e, y o u c a n s e e o n l y e v e n n u m b e r i n t e g e r s s q u a r e c a n h a v e e v e n n u m b e r a t u n i t p l a c e . S o, p i s a n e v e n i n t e g e r . o r y o u c a n p r o v e i t a s : - L e t p^{2} = 4 q i . e . a n e v e n i n t e g e r p = \sqrt{4 q} p = 2 \sqrt{q} T h e r e f o r e, p i s a l s o a n e v e n i n t e g e r .$

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