MathLiveFundamental theorem of arithmetic
Every integer greater than 1 (up to sign) can be written as a product of prime powers in exactly one way, apart from the order of the factors. The formula expresses an integer a as a signed product of distinct primes p_i raised to positive exponents e_i.
a=\pm p_1^{e_1}p_2^{e_2}\cdots p_r^{e_r}What the symbols mean
| a nonzero integer other than 1 and -1 | |
| distinct prime numbers | |
| positive integer exponent of the prime p_i | |
| number of distinct prime factors of a |
About this formula
- FieldMathematics
- TopicNumber theory
- LevelUniversity
- Also calledunique prime factorization theorem, unique factorization theorem, FTA, prime factorization theorem, prime factorisation theorem, unique factorisation theorem
- SourceWikidata Q670235
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