A338799 Smallest number that is the sum of two n-th powers of primes in two different ways.

10, 338, 6058655748, 3262811042

Offset: 1

Author

Ilya Gutkovskiy, Nov 10 2020

Keywords

• nonn
• hard
• more

Comments

The Lander, Parkin, and Selfridge conjecture implies that for n >= 5 a number can be the sum of two n-th powers of positive integers in at most one way, and in particular that a(n) does not exist for n >= 5. - Robert Israel, Nov 13 2020

Examples

			10 = 3 + 7 = 5 + 5.
338 = 7^2 + 17^2 = 13^2 + 13^2.
6058655748 = 61^3 + 1823^3 = 1049^3 + 1699^3.
3262811042 = 7^4 + 239^4 = 157^4 + 227^4.
		

Links

• Wikipedia, Lander, Parkin, and Selfridge conjecture.

Crossrefs

Cf. A016078, A046881, A338800.