123 is a peculiar integer, because 1+2+3=1*2*3. 1412 is also peculiar, since 1+4+1+2=1*4*1*2.

A simple question: are there infinitely many such numbers?

A not so simple question: if so, are there such numbers for ANY number of digits?

Any 2, 3, 4, etc digits between 2 and 9 can be chosen, and their product found. Intersperse as many 1's as needed to bring the total up to this product. (In the case of 2 and 2 no 1's will be needed.) This guarantees infinitely many such numbers.

Posted by Charlie on 2006-08-21 09:52:08