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Find all possible congruence classes x mod 6 such that 2x + 3 = −1 (mod 6).

Find all possible congruence classes x mod 6 such that 2x + 3 = −1 (mod 6).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 7:** Find all possible congruence classes \( x \mod 6 \) such that \( 2x + 3 \equiv -1 \pmod{6} \). --- This problem requires finding the values of \( x \) modulo 6 that satisfy the given linear congruence equation. You need to determine which integer values \( x \), when plugged into the equation \( 2x + 3 \equiv -1 \pmod{6} \), result in a true statement. The equation can also be interpreted as finding \( x \) such that \( 2x + 3 \) and \( -1 \) have the same remainder when divided by 6.
Transcribed Image Text:**Problem 7:** Find all possible congruence classes \( x \mod 6 \) such that \( 2x + 3 \equiv -1 \pmod{6} \). --- This problem requires finding the values of \( x \) modulo 6 that satisfy the given linear congruence equation. You need to determine which integer values \( x \), when plugged into the equation \( 2x + 3 \equiv -1 \pmod{6} \), result in a true statement. The equation can also be interpreted as finding \( x \) such that \( 2x + 3 \) and \( -1 \) have the same remainder when divided by 6.
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