31 Thirty-One XXXI
... divisors of two different numbers, 16 and 25. In fact, 31 = 1+2+4+8+16 = 1+5+25. (Number Gossip) No other numbers less than a million have this property Note that 31 = 1 + 5 + 52 = 1 + 2 + 22 + 23 + 24 is the sum of at least three successive powers, starting with 1, in two different ways. The only o ...
... divisors of two different numbers, 16 and 25. In fact, 31 = 1+2+4+8+16 = 1+5+25. (Number Gossip) No other numbers less than a million have this property Note that 31 = 1 + 5 + 52 = 1 + 2 + 22 + 23 + 24 is the sum of at least three successive powers, starting with 1, in two different ways. The only o ...
a review sheet for test #7
... unequal. In this case, you can also solve the quadratic equation by factoring. 2. If b2 – 4ac is positive but not a perfect square, then there are two solutions that are real, irrational, and unequal. 3. If b2 – 4ac = 0, then there is just one solution (a repeated root) that is real and rational (or ...
... unequal. In this case, you can also solve the quadratic equation by factoring. 2. If b2 – 4ac is positive but not a perfect square, then there are two solutions that are real, irrational, and unequal. 3. If b2 – 4ac = 0, then there is just one solution (a repeated root) that is real and rational (or ...
Factorization algorithms
... give the full prime factorization of a number. Fermat’s factorization. It is an extremely simple method essentially based on the relation x2 − y 2 = (x − y)(x + y). If we can find y such that n + y 2 = x2 then (x − y)|n. The following program uses this technique to obtain a nontrivial factor. Some l ...
... give the full prime factorization of a number. Fermat’s factorization. It is an extremely simple method essentially based on the relation x2 − y 2 = (x − y)(x + y). If we can find y such that n + y 2 = x2 then (x − y)|n. The following program uses this technique to obtain a nontrivial factor. Some l ...
