Cube And Square

Number Theory Level 1

If a integer is added by 1, it becomes a perfect cube. If it is subtracted by 1, it becomes a perfect square. Find the SMALLEST such number ?


The answer is 26.

Anish Harsha by Anish Harsha , 20, India

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5 solutions

We have to do this by trial and error.We get the answer as 26 \boxed{26}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

"Added by 1" is not a standard way of expressing the information. It would be "if one is added to the number." But below is my concise English version of the above problem statement.

"Find the smallest number a a such that a + 1 a+1 is a perfect cube and a − 1 a-1 is a perfect square."

Marta Reece - 3 years ago

Is there anyone who has come up with a strictly mathematical solution except for guessing?

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Galen Buhain
Nov 25, 2016

I just try the smallest perfect cubes like 8 and 27. If 7 is the answer, the 6 is not a perfect square. 26 is the answer because 25 is a perfect square...

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Kandarp Singh
Nov 1, 2014

it is a hit and trail method do by natural thinking 26 is the answer

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Riccardo Bassi
Nov 1, 2014

27=3^3; 25=5^2--> n=26

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