Daily Problem Solving

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… Read More »Solution to Problem of the Day – 01