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Question

Write cubes of 5 natural numbers which are of the form 3n+1 (e.g. 4,7,10,....) and verify the following:
'The cube of a natural number of the form
3n+1 is a natural number of the same form'.

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Solution

The 5 natural number which are of the form 3n+1 (e.g 4,7,10,....) are as follows:
3×1+1=3+1=4
3×2+1=6+1=7
3×3+1=9+1=10
3×4+1=12+1=13
3×5+1=15+1=16
The cubes of 5 natural numbers which are of the form
3n+1 (e.g. 4,7,10,....) are as follows:
(4)3=4×4×4=64
(7)3=7×7×7=343
(10)3=10×10×10=1000
(13)3=13×13×13=2197
(16)3=16×16×16=4096
Verification:
64=3×21+1
343=3×114+1
1000=3×333+1
2197=3×732+1
4096=3×1365+1
'The cube of a natural number of the form 3n+1 is a natural number of the same form'

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