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10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, = 5 has two divisors (1 and 5 itself) 6 = : 2 x 3 has four divisors (1, 2, 3 and 6) 16 = 2* has five divisors (1, 2, 4, 8 and 16). a2 az a, "where X Pk If a number n = p,' P2' P3 Pk-1' P¿are prime a d2 dz .. -1' a,are the corresponding exponents of the prime numbers, how x P2 X P3 k-1 numbers and many divisors does n have ?

10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, = 5 has two divisors (1 and 5 itself) 6 = : 2 x 3 has four divisors (1, 2, 3 and 6) 16 = 2* has five divisors (1, 2, 4, 8 and 16). a2 az a, "where X Pk If a number n = p,' P2' P3 Pk-1' P¿are prime a d2 dz .. -1' a,are the corresponding exponents of the prime numbers, how x P2 X P3 k-1 numbers and many divisors does n have ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, 5 has two divisors (1 and 5 itself) 6 = - 2' x 3* has four divisors (1, 2, 3 and 6) 16 = 2* has five divisors (1, 2, 4, 8 and 16). dk-1 If a number n = p,' хр 3 numbers and a,, a,, a̟. a_, a are the corresponding exponents of the prime numbers, how many divisors does n have ?
Transcribed Image Text:10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, 5 has two divisors (1 and 5 itself) 6 = - 2' x 3* has four divisors (1, 2, 3 and 6) 16 = 2* has five divisors (1, 2, 4, 8 and 16). dk-1 If a number n = p,' хр 3 numbers and a,, a,, a̟. a_, a are the corresponding exponents of the prime numbers, how many divisors does n have ?
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