Question

Using Euclid division lemma, Prove that positive integers CANNOT be in the form of 5m+2 or 5m+3

Answer 1

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Answer 2

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let a be any positive integer,

by Euclid's division lemma,

a=b q+r

a= 5 q+r

r=0,1,2,3,4

case 1:

a=b q +r

a=5 q +0  ⇒ 5 m 1⇒divisible by 5

case 2 :

a= b q +r

a=5 q +1

case 3 :

a=5q+2

a=5q +3

a=5q+4

a=5q+5 ⇒5(q+1)⇒divisible by 5