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A number which is simultaneously octagonal and triangular. Let O_n denote the nth octagonal number and T_m the mth triangular number, then a number which is both octagonal ...

1. Zero is a number. 2. If a is a number, the successor of a is a number. 3. zero is not the successor of a number. 4. Two numbers of which the successors are equal are ...

Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the ...

The partial differential equation u_t+u_(xxxxx)+30uu_(xxx)+30u_xu_(xx)+180u^2u_x=0.

The Latin prefix quadri- is used to indicate the number 4, for example, quadrilateral, quadrant, etc. However, it also very commonly used to denote objects involving the ...

The Frobenius number is the largest value b for which the Frobenius equation a_1x_1+a_2x_2+...+a_nx_n=b, (1) has no solution, where the a_i are positive integers, b is an ...

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in oblate spheroidal coordinates.

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in prolate spheroidal coordinates.

A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...