Add 1 and it's a composite number!

Number Theory Level 2

I have a favorite number, which is a 2-digit positive integer.

If I add 1 to this number, then it is divisible by 2.
If I add 1 to this number again, then it is divisible by 3.
If I add 1 to this number yet again, then it is divisible by 4.
If I add 1 to this number once more, then it is divisible by 5.

What is my favorite number?

The answer is 61.

1 solution

Sabhrant Sachan
Dec 27, 2016

Let Pi Han Goh's favorite number be $N$ . I am starting with the $4$ th condition here, keeping the $3$ rd in mind. Only odd integral multiples of $5$ are taken because $N+3$ should be even .

$N+4$ is divisible by $5$ : $15,25,35,45,55,65,75,85,95$

$N+3$ is divisible by $4$ : $24,44,64,84$

$N+2$ is divisible by $3$ : $63$

$N+1$ is divisible by $2$ : $62$

$\boxed{N=61}$

Add 1 and it's a composite number!

The answer is 61.

1 solution

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