You have probably all seen or read about Fermat receiving a letter asking if 100895598169 is prime and quickly replying that it was a factor of 112303 and 898423.
Anyway, I was trying to find out how he worked it out. Knowing the answers gives a huge help in finding a method, but don't think he did it the same way.
100895598169 X 8 = 807164785352
Sqrt of 807164785352 = 898423
100895598169 / 898423 = 112303
Can anyone come up with other methods ?