They discuss topics like what prime numbers are, division and multiplication, congruences,

Euler's theorem, testing for primality and factorization, Fermat numbers, perfect numbers, the Newton binomial formula, money and primes, cryptography, new numbers and functions, primes in arithmetic progression, and sequences, with examples, some proofs, and biographical notes about key mathematicians.

Mathematical justification for rotations on the sphere is an

Euler's theorem.

However, the only parameters available are those of the azimuth and elevation--by means of which it is possible to calculate the desired parameters (transformation matrices and

Euler's Theorem will be used for this) [9].

O'Hara's streamlined proof is in fact a direct generalization of Glaisher's classical bijection proving Euler's theorem.

Consider the classical Euler's theorem on partitions into distinct and odd parts.

Sections 3 and 4 examine the Marshallian credentials of two of Flux's economic writings: his famous review of Philip Wicksteed's 1894 Essay on the Coordination of the Laws of Distribution, which introduced Euler's theorem into the discussion of this problem: and, secondly, his Economic Principles (first edition, 1904; second edition, 1923).

In true Marshallian style, it concluded with a mathematical appendix containing diagrams and algebraic demonstrations of several economic propositions, including a simplified version of the use of Euler's theorem for solving the problem of general distribution as initially analysed by Wicksteed (Flux 1904, 1923, pp.

Coverage progresses from

Euler's theorem through Ferrers boards and unsolved problems.

This list is related to the number of vertices, faces and edges of the large cube, giving an example of

Euler's theorem that

Textbook theory assumes pure competition and uses

Euler's theorem to conclude that labor and capital are paid the value of their marginal product.

The class then generated

Euler's theorem, and the students were asked to test it.

The idea of the book was to follow the historical development of the proof of a single mathematical theorem,

Euler's Theorem, and to "show" that it did not really succeed in establishing the theorem beyond doubt.