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show that any positive odd integer is of the form 4q+1 or 4q+3 where q is some integer

Posted by Bharani Ajith 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years ago

Let a be any positive integer
by EDL a = bq +r
0 ≤ r < b
possible remainders are 0, 1, 2 , 3
this shows that a can be in the form of 4q, 4q+1, 4q+2, 4q+3 q is quotient
as a is odd a can't be the form of 4q or 4q+2 as they are even
so a ill be in the form of 4q + 1 or 4q+3
hence proved

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CBSE > Class 10 > Mathematics