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. are the corresponding angles congruent 2. find the ratios of the corresponding sides 3. is triangle jkl congruent to triangle rst? if so what is the scale factor

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?

Find the directions in which the function increases and decreases most rapidly at upper p 0p0. then find the derivatives of the function in these directions. f(x,y)equals=x squared plus xy plus y squaredx2+xy+y2, upper p 0p0left parenthesis 1 comma negative 4 right parenthesis