perplexus.info :: Just Math : Power to factorial

Power to factorial (Posted on 2023-08-13)

Find all non-negative integer solutions x,y,z,n that satisfy the equation

2^x + 5^y - 31^z = n!

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 4.0000 (1 votes)

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Solutions; not certain if complete

| Comment 1 of 3

(x,y,z,n,n!)

(0,0,0,0,1)

(1,0,0,2,2)

(1,1,0,3,6)

(3,2,1,2,2)

(5,0,1,2,2)

(5,1,1,3,6)

------------

def fact(n):

if n == 1 or n == 0:

return 1

ans = 1

for i in range(n):

ans *= (i+1)

return ans

factorials = [fact(i) for i in range(100)]

big = 100

print('(x,y,z,n,n!)')

for x in range(big):

for y in range(big):

for z in range(big):

f = 2**x + 5**y - 31**z

if f<1:

continue

if f in factorials:

print('({},{},{},{},{})'.format(x,y,z,factorials.index(f),f))

Posted by Larry on 2023-08-13 13:03:07

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