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From Catalan's theorem, we know that \(3^2 - 2^3 = 1\) is the only solution to the following equation, for some integers \(a,b \geq 1\) and ...

What is the remainder when \(7^{777}\) is divided by 2801?

Note: 2801 is prime.

\[2^a = 13^b + 2\cdot 7 \cdot 13 - 7^c\]

Given \(a,b,c\) be positive integers larger than 1, what is the least possible sum of ...

A baumkuchen or split cake has a hollow unit circular area in the middle with successive ring with the same unit radius, in which the first ring is divided equally ...

A famous chocolate shop sells the delicate Choco balls in \(3\) different packages: a small square box of \(9\) Choco balls, a middle hexagonal box of \(14\), and a large ...

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