Question

a) Show that for any integer x, its fourth power x^4 has remainder 0 or 1...

a) Show that for any integer x, its fourth power x^4 has remainder 0 or 1 when divided by 8.

b) Show that x^4 + y^4 + z^4 ≠ 5510 for any integer x,y,z

Homework Answers

Answer #1

In case of any doubt please ask in the comment section

Please upvote if satisfied

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Power(y: number; z: non-negative integer) 1. if z==0 then return 1 2. if z is odd...
Power(y: number; z: non-negative integer) 1. if z==0 then return 1 2. if z is odd then 3.      return (Power(y*y, z/2)*y) comment: z/2 is integer division; note the parentheses else 4.      return Power(y*y, z/2)          comment: z/2 is integer division Draw the Recursion Tree of Power(5,5)
4. 3323 A prime number can be divided, without a remainder, only by itself and by...
4. 3323 A prime number can be divided, without a remainder, only by itself and by 1. Write a code segment to determine if a defined positive integer N is prime. Create a list of integers from 2 to N-1. Use a loop to determine the remainder of N when dividing by each integer in the list. Set the variable result to the number of instances the remainder equals zero. If there are none, set result=0 (the number is prime)....
(a) Use modular arithmetic to show that if an integer a is not divisible by 3,...
(a) Use modular arithmetic to show that if an integer a is not divisible by 3, then a 2 ≡ 1 (mod 3). (b) Use this result to prove that in any Pythagorean triple (x, y, z), either x or y (or both) must be divisible by 3
1. Let p be any prime number. Let r be any integer such that 0 <...
1. Let p be any prime number. Let r be any integer such that 0 < r < p−1. Show that there exists a number q such that rq = 1(mod p) 2. Let p1 and p2 be two distinct prime numbers. Let r1 and r2 be such that 0 < r1 < p1 and 0 < r2 < p2. Show that there exists a number x such that x = r1(mod p1)andx = r2(mod p2). 8. Suppose we roll...
#mod reset; param T > 0, integer; set IND := 1..T; set END := 0..T+1; param...
#mod reset; param T > 0, integer; set IND := 1..T; set END := 0..T+1; param a >= 0; param b >= a; param c <= a; param r >= 0; param s >= 0; param d {IND} >= 0; var X {IND} >= 0, <= r; var Y {IND} >= 0, <= s; var Z {END} >= 0; minimize COST: sum {i in IND} (a * X[i] + b * Y[i] + c * Z[i]); subject to BAL {i...
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that...
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x, y) ≥ 0 for all (x, y). Hint: find the minimum value of H. (4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin is a critical point for f which is a saddle point, even though on any line through the origin, f has a local minimum at (0, 0)
For any odd integer n, show that 3 divides 2n+1. That is 2 to the nth...
For any odd integer n, show that 3 divides 2n+1. That is 2 to the nth power, not 2 times n
use the squeeze theorum to show that *** please show work limx→0 cos(x)x^8 sin(1/x)=0 limx→0 tan(x)x^4...
use the squeeze theorum to show that *** please show work limx→0 cos(x)x^8 sin(1/x)=0 limx→0 tan(x)x^4 cos(2/x)=0
Show that the two lines with equations (x, y, z) = (-1, 3, -4) + t(1,...
Show that the two lines with equations (x, y, z) = (-1, 3, -4) + t(1, -1, 2) and (x, y, z) = (5, -3, 2) + s(-2, 2, 2) are perpendicular. Determine how the two lines interact. Find the point of intersection of the line (x, y, z) = (1, -2, 1) + t(4, -3, -2) and the plane x – 2y + 3z = -8.
Let f(x, y) = (2y-x^2)(y-2x^2) a. Show that f(x, y) has a stationary point at (0,...
Let f(x, y) = (2y-x^2)(y-2x^2) a. Show that f(x, y) has a stationary point at (0, 0) and calculate the discriminant at this point. b. Show that along any line through the origin, f(x, y) has a local minimum at (0, 0)