context: A large body of mathematical work would still be valid when calling 1 a prime, but Euclid's fundamental theorem of arithmetic (mentioned above) would not hold as stated. For example, the number 15 can be factored as 3 · 5 and 1 · 3 · 5; if 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified. Similarly, the sieve of Eratosthenes would not work correctly if 1 were considered a prime: a modified version of the sieve that considers 1 as prime would eliminate all multiples of 1 (that is, all other numbers) and produce as output only the single number 1. Furthermore, the prime numbers have several properties that the number 1 lacks, such as the relationship of the number to its corresponding value of Euler's totient function or the sum of divisors function.
question: సంఖ్య 1 ను అభాజ్యంగా పరిగణించినట్లయితే ఏ సిద్ధాంతం చెల్లదు?
answers: Euclid's fundamental theorem of arithmetic Euclid's fundamental theorem of arithmetic arithmetic Euclid's fundamental theorem of arithmetic Euclid's fundamental theorem of arithmetic