Mutahdbban (amicable numbers), i, e.

Mutahdbban (amicable numbers), i, e., two such numbers in which the sum of the divisors of one equal the other, e.g., 220 and 284: 1+2+4+71+142=220 1+2+4+5+10+11+20+22+44+55+110=284.

(iv) Muthallathat (triangular numbers), e.g., the numbers 1, 3, 6, 10, 15, 21, 28, 36, 45, which are the sum of the first one, first two, first three, first four and so on, natural numbers.[^2] The Arabs also solved the famous problem of finding a square which, on the addition and subtraction of a given number, yields other squares.[^3] The extent of their knowledge of arithmetic can be gauged from the fact that al-Biruni was able to give the correct value of 1616-1.[^4] C - Algebra The ancient mathematicians, including the Greeks, considered the number to be a pure magnitude.

It was only when al-Khwarizmi (d. 236/850) conceived of the number as a pure relation in the modern sense that the science of algebra could take its origin. The development of algebra is one of the greatest achievements of the…