Research Links Fermat–Euler theorem Euler's totient function Fermat's little theorem Proofs of Fermat's little theorem Proof of Fermat's Little Theorem Chinese remainder theorem Eulers Theorem – a more general version that only specifies coprime requirement instead of prime requirement. Fermat's little theorem states that if p is a prime number, then for any integer a, the Read more…
If you have the product of two numbers and want to calculate the modulus of said product Where A,B and C are integers let where a & b are the modulus of A & B respectively and m & n are integers Substituting: and because everything is an integer Read more…
Research Links 536 Puzzles and Curious Problems A man entered a store and spent one-half of the money that was in his pocket. When he came out he found that he had just as many cents as he had dollars when he went in and half as many dollars as Read more…
A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly Read more…
Research Links 536 Puzzles and Curious Problems The clerks attached to the finn of Pilkins and Popinjay arranged that three of them would lunch together every day at a particular table so long as they could avoid the same three men sitting down twice together. The same number of clerks Read more…
Research Links Wikipedia: LaGrange Multiplier The Maximum Entropy Principle – The distribution with the maximum entropy is the distribution nature chooses Maximum Entropy Distribution for Random Variable of Extent [0,Infinity] and a Mean Value Mu Derivation of Nyquist 4KTBR Relation using Boltzmann 1/2KT Equipartition Theorem Derivation of the Normal Gaussian Read more…
Research Links 536 Puzzles and Curious Problems The Crackhams made their first stop at Bugleminster, where they were to spend the night at a friend's house. This friend was to leave home at the same time and ride to London to put up at the Crackhams' house. They took the Read more…
Research Links 536 Puzzles and Curious Problems Complete Solution
Research Links 536 Puzzles and Curious Problems This is what the author called a trick question. The sum of the distances are constant. To see why draw in lines from the vertices of the original triangles forming subtriangles T1,T2,T3. Now the sum of the areas of T1,T2,T3 = area Read more…
The solutions giving in the book 536 Puzzles and Curious Problems are quite shorthanded and in order to understand them often you have to dig. Since in a right triangle: and area we can substitute and get Now since we can substitute in which Read more…