Question

Prove that every natural number can be written in form of 5k or 5k+1 or 5k+2​

Answer 1

Step-by-step explanation:

Yes it can be proven by the following method:

Let 'a' be any natural number and 'b' =5

We know that;

a = bq + r ( where 0 {< or =}r < b )

therefore, r = 0 ,1 ,2 ,3 , or 4

• if r = 0 ,

then, a = 5q + 0

a = 5(q)

a = 5k. ( where k is any positive integers)

• if r = 1,

then, a = 5q + 1

a = 5(q +1)

a = 5k . ( where k is any positive integers)

• if r = 2 ,

then, a = 5q + 2

a = 5(q + 1) + 1

a = 5k +1. ( where k is any positive integers)

• if r = 3 ,

then, a = 5q + 3

a = 5(q + 1) + 2

a = 5k + 2. ( where k is any positive integers)

• if r = 4 ,

then, a = 5q + 4

a = 5(q + 2) + 2

a = 5k + 2. ( where k is any positive integers)

Therefore, any natural number is in the form of :

5k, 5k + 1 or 5k + 2