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Euclid lemma

Euclid

Euclid lemma was first discovered by the Greek mathematician Euclid. Euclid lemma is the fundamental proof for the prime numbers. Prime numbers are the important numbers in mathematics that are divisible only by one or the number itself.

Euclid lemma states that, 'if the product of the two numbers are divisible by a prime number, than one of the two numbers or both the numbers are divisible by the same prime number'.

For example,

Let us consider two integers a and b. Also let the product of ab is divisible by prime number p. Then the prime number p must divide a or b or both a and b.

9 x 4 = 36.

Here 36 is divisible by the prime number 9 and 3. 9 is also divisible by 3 and 9.

This property of prime numbers are the important proof of unique prime factorization theorem. Prime lemma is not applicable for any composite numbers.

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