p be a prime number. Show that for any integer a the greatest common divisor of p and a is either p (if pla) or is 1 (if p does not divide a).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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(1) Let p be a prime number. Show that for any integer a the greatest common divisor
of p and a is either p (if pla) or is 1 (if p does not divide a).
Transcribed Image Text:(1) Let p be a prime number. Show that for any integer a the greatest common divisor of p and a is either p (if pla) or is 1 (if p does not divide a).
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An integer 'n' is called a factor or a divisor of another integer 'm' if 'n' divides 'm' exactly and in such a case 'm' is called a multiple of 'n'.

A natural number greater than 1, that has exactly two factors, i.e., 1 and the number itself, is called a prime number. e.g. 2, 3, 5, 7, 11, 13, etc.

Any number that has more than two factors (i.e. other than itself and the number 1) is called a composite number. e.g. 4, 6, 8, etc.

Note: 2 is the only even prime number. 1 is neither prime nor composite.

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