Write whether every positive integers can be of thenform 4q+2 whereq is an integer justify your answer
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Let a be any positive even integer.
By Euclid's division lemma,
a=bq+r where,"b" is greater then "r" is equal to or greater then "0"
a=4q+r
a=4q + r where,. (r=0,1,2,3). .........(1)
put r=0 in equation (1)
a=4q+0
a=4q (which is even)
put r=1 in equation (1)
a=4q + 1. (which is odd)
put r=2 in equation (1)
a=4q+2 (which is even)
put r=3 in equation (1)
a=4q+3 (which is odd)
hence,
every positive even integer is in the form of 4q,4q+2, where "q" is an intiger.
By Euclid's division lemma,
a=bq+r where,"b" is greater then "r" is equal to or greater then "0"
a=4q+r
a=4q + r where,. (r=0,1,2,3). .........(1)
put r=0 in equation (1)
a=4q+0
a=4q (which is even)
put r=1 in equation (1)
a=4q + 1. (which is odd)
put r=2 in equation (1)
a=4q+2 (which is even)
put r=3 in equation (1)
a=4q+3 (which is odd)
hence,
every positive even integer is in the form of 4q,4q+2, where "q" is an intiger.
Amankumarvishwakarma:
tum sayad "even" likhne bhul gya h
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