Fermat's theorem implies that 2-1)/2 = +1 (mod p).] 11. apply theorem 5.5 to obtain two solutions to each of the quadratic congruences x -1 (mod 29) and x = -1 (mod 37). 12. show that ilp - 4k+ 3 is prime and a + b 0 (mod p), then amb0 (mod p). hint: if a 0 (mod p), then there exists an integer c such that ac i (mod p); use this fact to contradict theorem 5.5.)
theorem 5.5. the quadratic congruence x + 1 = 0 (mod p), where p is an odd prime, has a solution if and only if p = 1 (mod 4).

1.0

step-by-step explanation:

3/5

step-by-step explanation:

double number line is not a standard concept, so it must have been defined in your textbook. assume top line is numerator.

step-by-step explanation:

when the line is solid:

when the line is dashed:

this > inequality sign means:

this < inequality sign means:

this > inequality sign means:

this < inequality sign means:

about the problem:

srry i'm not done ! i'll

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)