is 10 solitary

Is 10 a solitary number?

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One of the the more famous unsolved problems in mathematics is the question of whether 10 is a solitary number.

Numbers which have no friendly pair are called 'solitary' numbers. If you read the page on friendly, or amicable numbers, then you would know that there are not that many of them - true friends are rare indeed. So most of the numbers are solitary! And it is pretty obvious that it may be a bit hard to prove for some big number whether it has a friendly pair or not, but would it be difficult to prove that 10 has no friendly pair? It may seem an easy thing to do, but no one has yet found a proof.

All primes and prime powers are solitary numbers. So far people have proved for some numbers that they are NOT solitary by finding their friendly pair. Sometimes the difference in pairs is very large: for example, 24 has a friendly pair in 91963648. But no such pair has ever been found for 10! You can try - if you don't know enough about friendly numbers, click here.

See a page about some famous theorems and conjectures, or about some of the famous solved problems from the history of mathematics.

Hilbert posed some 23 mathematical problems back in 1900. Some of them have been solved, but some haven't. Learn about them and try to solve them, and if you succeed, you may become very famous and very wealthy!

Learn more about Hilbert by clicking on his picture.

Of course, the most famous of all the theorems is Pythagoras' Theorem. Click on his picture to find more about him.

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