Question

1. Find all solutions of the congruence $x^2 + x - 1 \equiv 0 \pmod{7}$ 2. Solve the simultaneous congruences $x \equiv 4 \pmod{5}$ and $2x \equiv 3 \pmod{7}$ 3. The congruence $129^{64026} \equiv 15179 \pmod{64027}$ Can you conclude that 64027 is a composite number? NOTE: Check the definition of a composite number 4. Solve the congruence $x^4 + 2x^2 + 4 \equiv 0 \pmod{7}$

          1. Find all solutions of the congruence
$x^2 + x - 1 \equiv 0 \pmod{7}$
2. Solve the simultaneous congruences
$x \equiv 4 \pmod{5}$ and $2x \equiv 3 \pmod{7}$
3. The congruence $129^{64026} \equiv 15179 \pmod{64027}$
Can you conclude that 64027 is a composite number?
NOTE: Check the definition of a composite number
4. Solve the congruence $x^4 + 2x^2 + 4 \equiv 0 \pmod{7}$

1. Find all solutions of the congruence
x^2 + x - 1 ≡ 0 7
2. Solve the simultaneous congruences
x ≡ 4 5 and 2x ≡ 3 7
3. The congruence 129^64026≡ 15179 64027
Can you conclude that 64027 is a composite number?
NOTE: Check the definition of a composite number
4. Solve the congruence x^4 + 2x^2 + 4 ≡ 0 7

Added by Keith U.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

12/11/2022

Step 1

Step 2: We can solve the simultaneous congruences x ≡ 4 (mod 5) and 2x ≡ 3 (mod 7) by using the Chinese Remainder Theorem or by substitution. Step 3: To determine if 64027 is a composite number, we can check if it has any factors other than 1 and itself. Step Show more…

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Find all solutions of the congruence x^(2)+x-1-=0(mod7) Solve the simultaneous congruences x-=4(mod5) and 2x-=3(mod7) The congruence 129^(64026)-=15179(mod64027) Can you conclude that 64027 is a composite number? NOTE: Check the definition of a composite number Solve the congruence x^(4)+2x^(2)+4-=0(mod7) 1. Find all solutions of the congruence x2 +x -1=0(mod7) 2. Solve the simultaneous congruences x =4(mod5) and 2x = 3(mod 7) Can you conclude that 64027 is a composite number? NOTE: Check the definition of a composite number 4. Solve the congruence x4 + 2x2 + 4 = 0 (mod 7)