Show that the square of any positive integer

Asked by admin @ 29/08/2021 in Math viewed by 333 People

Prove that square of any positive integer is of the form 4q or 4q+1 for some integer q

Answered by admin @ 29/08/2021

Let 'a' be any positive integer.
b=4
by Euclid's division lemma,
a=bq+r
a²=(bq+r)²-------1.
r=0,1,2,3
from 1.
for r=0,
a²=(4q+0)²
a²=16q²
a²=4(4q²)
=4q, where q=4q².
for r=1,
a²=(4q+1)²
a²=16q²+1+8q
a²=4(4q²+2q)+1
a²=4q+1, where q=4q²+2q.

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Asked by admin @ 20/08/2021 in Math viewed by 306 persons

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Asked by admin @ 17/08/2021 in Chemistry viewed by 305 persons

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Asked by admin @ 17/08/2021 in Math viewed by 278 persons

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