Question

Show that every positive integer can be expressed can be expressed as 3q or 3q+1 or 3q+2 or 4q+3.For some integer 'q'
please answer the question!

Answer 1

Hey!!!!

Answer ⤵️

let a be any positive integer

let b = 3(divisor)

By Euclid's Division Lemma,

=> a = 3q + r where 0 =< r < b

Case 1
r = 0

Then a = 3q

Case 2 r = 1

Then a = 3q + 1

Case 3 r = 2

Then a = 3q + 2

Now b = 4

Similarly a = 4q + r

Case 4 r = 3

Then a = 4q + 3

HENCE PROVED

Hope this helps