perplexus.info :: Just Math : Product of consecutive

Product of consecutive (Posted on 2024-09-11)

Find all integers n such that n⁴-8n+15 is product of two consecutive integers.

No Solution Yet Submitted by Danish Ahmed Khan

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| Comment 2 of 3 |

Testing for n up to 10^6, I found the same 2 solutions as Charlie.

n f(n)

3 72 = 8*9

5 600 = 24*25

-----------

def f(n):

return n**4 - 8*n + 15

big = 1000000

conprods = [k*(k+1) for k in range(big)]

for n in range(big):

if f(n) > conprods[-1]:

print('too big', conprods[-1],n, f(n))

break

if f(n) in conprods:

print(n, f(n), int(f(n)**.5))

Posted by Larry on 2024-09-11 11:23:08

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