Question

show that every positive integer can be written in the form 3m+r,where m and r are positive integers.what values can r take?

Answer 1

By Euclid division Lemma,given two positive integers a and b, there exist
unique integers m and r satisfying

a = bm + r, 0 ≤ r < b.

Let b=3
Then r can be 0,1,2
Then By Euclid division lemma as

a can be 3m or 3m+1 or 3m+2.

Thus,every positive integer can be written in the form 3m+r,where r = (0,1,2)

Answer 2

Answer:By Euclid division Lemma,given two positive integers a and b, there exist

unique integers m and r satisfying

a = bm + r, 0 ≤ r < b.

Let b=3

Then r can be 0,1,2

Then By Euclid division lemma as

a can be 3m or 3m+1 or 3m+2.

Thus,every positive integer can be written in the form 3m+r,where r = (0,1,2)

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