a)
The functions y1 = x^2 and y2 = x^5 are
two solutions of the equation
x^2 y ″ − 6 x y ′ + 10 y = 0.
Let y be the solution of the equation x^2 y ″ − 6 x y
′ + 10 y = 3 x^5
satisfyng the conditions y ( 1 ) = 0 and y ′ ( 1 ) =
1.
Find the value of the function f ( x ) = y ( x )...
let p = 1031, Find the number of solutions to the equation x^2
-2 y^2=1 (mod p), i.e., the number of elements (x,y),
x,y=0,1,...,p-1, which satisfy x^2 - 2 y^2=1 (mod p)