Solution to Problem of the Day – 01

Problem Statement


Solution

$1111$ divides both $2222$ and $5555$ individually.

$1111 = 11*101$

Since both are primes, any of them are the answer.

Again,

${2222}^{5555} +{5555}^{2222}$

$≡{(2223-1)}^{5555}+{(5556-1)}^{2222}$

$≡{(-1)}^5+{(-1)}^2$

$≡-1+1$

$≡ 0$

$(mod\text{ } 3)$


So, the given number is also divisible by $3$, which happens to be a prime.


Hence, any of the following primes
$3$, $11$ and $101$ can be a prime factor of the given number.


Proposed by,

Ihfaz Ahmed Adib

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