Exercise · ZW-MODULAR-CONGRUENCE-007 · ★★☆ Intermediate
Solve \(3x\equiv4\pmod7\) with \(0\le x\le6\).
Choose one option.
Show answer
- C. 6
Explanation
Trying values: \(3\cdot6=18=2\cdot7+4\), so \(x=6\). No other residue works: \(3\cdot5\equiv1\), \(3\cdot4\equiv5\), \(3\cdot2\equiv6\).
Review the concept: Modular congruence
Two integers \(a\) and \(b\) are congruent modulo a positive integer \(m\) if \(m\) divides their difference; equivalently, they leave the same remainder when divided by \(m\).
\[a\equiv b\pmod m\iff m\mid(a-b)\]
More practice problems: modular congruence
- ZW-MODULAR-CONGRUENCE-001 Which of the following congruences is true?
- ZW-MODULAR-CONGRUENCE-002 Compute 53bmod8.
- ZW-MODULAR-CONGRUENCE-003 What is -7bmod5?
- ZW-MODULAR-CONGRUENCE-004 Compute (17+25)bmod6.
- ZW-MODULAR-CONGRUENCE-005 Compute 3^4bmod5.
- ZW-MODULAR-CONGRUENCE-006 Compute 2^10bmod7.
- ZW-MODULAR-CONGRUENCE-008 What is the last digit of 7^2026?
- ZW-MODULAR-CONGRUENCE-009 If a≡ b and c≡ dpmod m, which statement does NOT always hold?