Is there any easy way to find the answer to the following problem without trying numbers one by one?
How many ordered triples of primes $(a, b, c)$ exist such that $a+b+c=37$?
Asked
Active
Viewed 482 times
0
learning
- 1,749
-
Actually, it wouldn't be hard to do a case check! W.L.O.G. $a \le b \le c$! Then $c\le 31$. Now substitute primes less that or equal to $31$ for $c$ and search for $a$ and $b$! – Ghartal Jun 03 '16 at 03:31
-
2The whole point of the sequence of exercises is for you to list carefully. The only real shortcut is that if for example you have found that $(7,13,17)$ works, then its $5$ relatives obtained by permuting also work. A similar comment can be made for $(3,3,31)$ (two others obtained by permuting). – André Nicolas Jun 03 '16 at 03:47