"America's Got Talent," season 14
1134 and 3825 are the new 735
(IV have left the chat)
(IV have left the chat)
Exponents count down: 5, 4, 3, 2, 1.
Everything here is prime, except those two 1s in 113 and those two 4s. But 1 is a kinda-sorta honorary prime-oid, and 4 is 2^2.
Anyway.
Is this already a known equation?
#NumberTheory
Exponents count down: 5, 4, 3, 2, 1.
Everything here is prime, except those two 1s in 113 and those two 4s. But 1 is a kinda-sorta honorary prime-oid, and 4 is 2^2.
Anyway.
Is this already a known equation?
#NumberTheory
= 2⁵ + 3⁵ + 12⁵ + 13⁵ + 14⁵
= 4⁵ + 7⁵ + 8⁵ + 9⁵ + 16⁵
= 2⁵ + 3⁵ + 12⁵ + 13⁵ + 14⁵
= 4⁵ + 7⁵ + 8⁵ + 9⁵ + 16⁵
83370010, which is the sum of fourth powers of primes six ways, five as ten fourth powers, and one as eleven fourth powers.
83370010
=17^4+19^4+23^4+29^4+31^4+43^4+47^4+61^4+67^4+79^4
=2^4+3^4+5^4+13^4+17^4+29^4+31^4+43^4+61^4+71^4+79^4
[1/2]
83370010, which is the sum of fourth powers of primes six ways, five as ten fourth powers, and one as eleven fourth powers.
83370010
=17^4+19^4+23^4+29^4+31^4+43^4+47^4+61^4+67^4+79^4
=2^4+3^4+5^4+13^4+17^4+29^4+31^4+43^4+61^4+71^4+79^4
[1/2]
A prime that cannot be expressed as the sum of three squares is nevertheless the sum of three cubes – three prime cubes – two ways, with all six prime summands distinct.
13^3 + 43^3 + 47^3 = 185527
19^3 + 31^3 + 53^3 = 185527
#NumberTheory #Mathematics #Primes #RecreationalMathematics
A prime that cannot be expressed as the sum of three squares is nevertheless the sum of three cubes – three prime cubes – two ways, with all six prime summands distinct.
13^3 + 43^3 + 47^3 = 185527
19^3 + 31^3 + 53^3 = 185527
#NumberTheory #Mathematics #Primes #RecreationalMathematics
= 227^2 + 229^2 + 809^2 + 811^2
= 179^2 + 181^2 + 821^2 + 823^2
= 149^2 + 151^2 + 827^2 + 829^2
= 521^2 + 523^2 + 659^2 + 661^2
#NumberTheory #RecreationalMath #TwinPrimes #Primes #Mathematics #DidEulerKnow
= 227^2 + 229^2 + 809^2 + 811^2
= 179^2 + 181^2 + 821^2 + 823^2
= 149^2 + 151^2 + 827^2 + 829^2
= 521^2 + 523^2 + 659^2 + 661^2
#NumberTheory #RecreationalMath #TwinPrimes #Primes #Mathematics #DidEulerKnow