By brute force: when the exponent is 666, the answer appears to be 1512.
I did some explorations:
For odd exponents, the answer is 2
For even exponents which are either 2 mod 12 or 10 mod 12, the answer is 24
When the exponent is 6* a prime, the answer is 504
Some multiples of 222:
exp gcd
222 504
444 5040
666 1512
888 10080
1110 504
1332 15120
1554 3528
1776 20160
1998 4536
2220 25200
-------
import math
import sympy
from itertools import combinations
def gcdList(aList):
ans = math.gcd(aList[0],aList[1])
for i,v in enumerate(aList):
if i < 2:
continue
ans = math.gcd(ans,v)
return ans
big = 10000
primes = [i for i in range(11, big) if sympy.isprime(i)]
for expo in range(666,667):
powers = [n**expo for n in primes]
diffs = []
for comb in combinations(powers,2):
diffs.append(comb[1] - comb[0])
print(expo, gcdList(diffs))
|
|
Posted by Larry
on 2025-02-02 13:43:10 |
Brute force
