This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the value of 2 ÷ 3 in (mod 4), we need to solve the congruence equation 3x 2 4. Step 1: Set up the congruence. We are looking for an integer x such that 3x leaves a remainder of 2 when divided by 4. 3x 2 4 Step 2: Find the multiplicative inverse of 3 4. We need to find an integer y such that 3y 1 4. Let's test values for y: • For y=0, 3 × 0 = 0 1 4 • For y=1, 3 × 1 = 3 1 4 • For y=2, 3 × 2 = 6 2 4 • For y=3, 3 × 3 = 9 1 4 The multiplicative inverse of 3 4 is 3. Step 3: Multiply both sides of the congruence by the inverse. Multiply both sides of 3x 2 4 by 3: 3 × (3x) 3 × 2 4 9x 6 4 Step 4: Simplify the congruence. Since 9 1 4 and 6 2 4, substitute these values into the congruence: 1x 2 4 x 2 4 The value of 2 ÷ 3 in (mod 4) is 2. That's 2 down. 3 left today — send the next one.