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Browse Classroom Capsules and Notes

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If one term is changed in the sum of cubes of positive integers, the formula for the sum varies similarly.

The partition function is modified so that summands must be prime integers.

The congruence \((a+b)^n \equiv a^n + b^n\) (mod \(n\)) when \(n\) is prime, or is a Carmichael number

This article revisits the famous calculus optimization problem of removing four corner squares from a sheet and folding up the edges to form a box of maximal volume. The authors analyze the...

The author uses the computer algebra system Maple to introduce a number of interesting investigations based on Newton's Method for finding roots of an equation.

The author investigates properties of "almost squares," rectangles with integer sides and area \(A\) such that the the perimeter is least among all rectangles with integer sides and...

Several tricks useful in mathematical competitions are discussed.

Non-integer square roots of integers are irrational.

The existence of an odd perfect number is related to the abundancy index.

All but finite numbers of integers can be written as a sum of \(N\) squares, where \(N\) is between 5 and 156.