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Wilson Junior wants to determine the least positive integer \(N\) such that \(N \equiv 82!!\, \bmod \,83\). He applied Wilson's theorem as follows: ...

The clock has the hour and minute hands. The hour hand is the shortest, whereas the minute hand is the longest.

Assume that all hands continuously and smoothly rotate throughout ...

\((1,5,2,3)\) are 4 distinct positive integers such that the sum of 2 of them equals the product of the other 2, and the converse is also true ...

Consider a sequence of positive reals

\[ a_1 = 2017, a_2, a_3, a_4, \ldots , \]

which satisfy \( a_{i+2} = a_{i} - a_{i+1} \) for all positive integers \(i\).

Let \(k\) be ...

In the country of Sopcraenne, there are \(n\,(\ge 61)\) airports built recently such that the distances between any two airports are all different from one another.

A plane will ...

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