Solving a 'Stanford' University entrance exam | m=? n=?

[@kathleenryan8545]

You gave me a headache! 🤕😳

[@davidseed2939]

For any question of this type. Find natural numbers a,b such that 1/a+1/b=1/c The solutions are a=b=2c and a=(c+1) . b=c(c+1) If sometimes helpful to look at an easier problem. c=2 1/2= 1/4+1/4 1/2=1/3+1/6

[@tassiedevil2200]

@davidseed2939 Actually the set of three solutions is not exhaustive unless c is a prime number. For example 1/m+1/n=1/12 has eight solution pairs for positive integers.

[@tassiedevil2200]

This problem, with the identical solution strategy, was posted back in November by "Math Beast". kzbin.info/www/bejne/m5rXk4GGj9WLhZIsi=L9mVmlGSPeOLfPN5

[@MiroslawNowicki-h1o]

I wish you learn speak Oxford english, ?