Fermat's right triangle theorem is, by the Pythagorean theorem, they would form two integer-sided right triangles in which the pair formula_10 gives one leg and the hypotenuse of the smaller triangle and the same pair also forms the two legs of the larger triangle. But if (as Fibonacci asserted) no square congruum can exist, then there can be no two integer right triangles that share two sides in this way. Because the congrua are exactly the numbers that are four times the area of a Pythagorean triangle, and multiplication by four does not change whether a number is square, the existence of a square
Hope (given name) in Church Latin and her name is translated differently in other languages. Faith, Hope and Charity, the three theological virtues, are names traditionally given to triplet girls, just as Faith and Hope remain common names for twin girls. There were 40 sets of twins named Faith and Hope born in the United States in 2009, the second most common name combination for twin girls. One example were the American triplets Faith, Hope and Charity Cardwell, who were born in 1899 in Texas and were recognized in 1994 by the Guinness Book of World Records as the world's longest lived triplets.