Question

Use Euclid division lemma to show that any positive odd integer is in the form of 5q+1, 5q+3

Answer 1

According to LEMMA

a=bq+r here 0<or=r<b

S put values here

a=5q+r

all remainders are possible i.e.

0,1,2,3,4.

all integers are possible i.e.

a=5q+0, Even

a=5q+1, Odd

a=5q+2, Even

a=5q+3, Odd

a=5q+4. Even.

Hence Proved.

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