ramannjit wrote:If a = 5^20-5^19+5^18, what is the length of a? (The length of an integer is the number of prime numbers, not necessarily distinct, in the prime factoriztion of the integer.)
Answer I got is correct, I am confused between when simply "length" is stated vs "maximum possible length". Help is needed in understanding the concept.
OA 20
Maximum possible length will be discussed only when the value of the integer is unknown. For example:
What is the maximum possible length of a positive integer less than 10?
Answer = 3, because 2*2*2 = 8, giving us 3 prime factors. If we add another prime factor, the product will become larger than 10.
In the problem above, the value of the integer is known, so all we have to do is count the number of prime factors:
5^20-5^19+5^18 = 5^18(5^2 - 5 + 1) = 5^18(21) = 5^18*3*7, giving us 18+1+1=20 prime factors. Thus, the length is 20.
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