Question

if p square is in is an even integer then prove that P is also an even integer​

Answer 1

Answer:

While reading a proof for √2 being irrational I came across below proof:

Suppose √2 = p/q where p and q are integers.

P2 = 2 q2 --> P is EVEN ( This line troubled me )

Let p =2 r

2 r2 = q2 --> Q must be EVEN

If both p and q are even so assumption is wrong, proving √2 is irratonal.

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So I thought if I could prove that if P2 is EVEN then P is EVEN.

My try:

Let P is EVEN ... P = 2n , where n is an integer .

p2 = 4 n2 = EVEN

Let P is ODD P= 2n+1 , where n is an integer .

P2 = (2n+1)2 = 4n2+4n+1 = 4(n2+n) + 1 = EVEN number +1 = ODD

Step-by-step explanation:

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