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(c) If p is a prime, then p¹3 will always have exactly fourteen positive divi- sors, namely: {1,p, p², p³,p4, p5, p6, p²,ps,pº, p¹0, p¹¹, p¹2, p¹³}. 10 11 12 Give an example of a number that is not a perfect thirteenth power of a prime but still has exactly fourteen positive divisors.

(c) If p is a prime, then p¹3 will always have exactly fourteen positive divi- sors, namely: {1,p, p², p³,p4, p5, p6, p²,ps,pº, p¹0, p¹¹, p¹2, p¹³}. 10 11 12 Give an example of a number that is not a perfect thirteenth power of a prime but still has exactly fourteen positive divisors.

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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13 (c) If p is a prime, then pl3 will always have exactly fourteen positive divi- sors, namely: {1,p.p², p³, p², p5, po, p²,ps,pº, p¹0, pl¹, p¹2, p¹³}. 12 ,plo Give an example of a number that is not a perfect thirteenth power of a prime but still has exactly fourteen positive divisors. 6
Transcribed Image Text:13 (c) If p is a prime, then pl3 will always have exactly fourteen positive divi- sors, namely: {1,p.p², p³, p², p5, po, p²,ps,pº, p¹0, pl¹, p¹2, p¹³}. 12 ,plo Give an example of a number that is not a perfect thirteenth power of a prime but still has exactly fourteen positive divisors. 6
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