I'm sure you'll know already but the × HTML entity should render the multiplication sign okay i.e. × vs x
These here should all work as they're from c. 2001, maybe the minus one is of use too?! Thanks! :o)
So you know that the minimum a, b or c can be is 2, since 1 is square. IF a = 2, then that means b = 2 * a square, and c = 2 * a square. This gives us 2, 2 * 4 and 2 * 9 = 2, 8, 18. Added together gives us 28.
However, the real trick is spotting that all of a, b and c must be multiples of squares, and all the same multiple of different squares. Otherwise the condition ab, bc and ca being squares won't work.
I'll let you work out how to see those bits, if not feel free to comment again and I'll explain :)
The multiplication is clearly a multiple of 4, since we have 2^2 at the start. This means that, when dividing by 8, we can only get either remainder 4 or 0. Since none of the other prime factors are divisible by 2, it means it is not divisible by 8, so it must be remainder 4!
Copyright H Brothers Inc, 2008–2023
| Go To Top
| View Mobile Site