Hankalaisluku

Hankalaisluku is a concept originating from Finnish mathematical folklore. It refers to a number that, when multiplied by itself, results in a number ending in the same digit as the original number. For example, 5 multiplied by 5 is 25, which ends in 5. Similarly, 6 multiplied by 6 is 36, which ends in 6. These numbers are also known as automorphic numbers.

The term "hankalaisluku" itself is not a formal mathematical term. It is believed to have been coined in informal discussions or perhaps in educational settings in Finland to describe this peculiar property of certain numbers. The word "hankala" in Finnish translates to "difficult" or "tricky," suggesting that the property might have been considered an interesting or slightly puzzling mathematical curiosity.

The simplest hankalaisluvut are the single-digit numbers 0, 1, 5, and 6. Beyond these, larger hankalaisluvut exist, such as 25 (25 * 25 = 625), 76 (76 * 76 = 5776), and 376 (376 * 376 = 141376). The pattern for these numbers is related to modular arithmetic, specifically looking for numbers x such that x^2 is congruent to x modulo 10^n, where n is the number of digits. While the name might be informal, the mathematical principle behind hankalaisluvut is a well-established area of number theory.