Question

write the cube of the five natural number of the form 3n+1 (eg. 4,7,10 ) and verify the following:
the cube of the natural number of form 3n +1 is a natural number of the same form i.e. when divided by three the remainder is 1​

Answer 1

Answer:

As we know that the first 5 natural numbers in the form of (3n + 1) are 4, 7, 10, 13 and 16

The cube of 4, 7, 10, 13 and 16

43 = 4 × 4 × 4

= 64

73 = 7 × 7 × 7

= 343

103 = 10 × 10 × 10

= 1000

133 = 13 × 13 × 13

= 2197

163 = 16 × 16 × 16

= 4096

Hence , all these cubes when divided by ‘3’ leaves remainder 1.

∴∴ “The cube of a natural number of the form 3n+1 is a natural number of the same from i.e. when divided by 3 it leaves the remainder 1’ is true.