Let p be an odd prime and let a be an integer with p - a.
(a) prove that a(p−1)/2 is congruent to either 1 or −1 modulo p.
(b) prove that a(p−1)/2 is congruent to 1 modulo p if and only if a is a quadratic residue modulo p. (hint. let g be a primitive root for p and usethefact,3.60,thatgm is a quadratic residue if and only if m is even.)
(c) prove that a(p−1)/2 ≡¡a p¢(mod p). (this holds even if p|a.)
(d) use (c) to prove theorem 3.61(a), that is, prove that

yes. we do proportions in probabilities.

where r the answers

step-by-step explanation:

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.

step-by-step explanation:

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