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Question 1087574: Find all replacements (less than the modulus) for the question mark that makes the statement true.
4 x ? = 3 (mod6)
1) 1,3,5
2) 0
3) 2,4
4) no solution
Found 2 solutions by jim_thompson5910, rothauserc:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let x be a variable
If x = 1, then
4*x = 4*1 = 4 (mod 6)
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If x = 2, then
4*x = 4*2 = 8 = 2 (mod 6)
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If x = 3, then
4*x = 4*3 = 12 = 0 (mod 6)
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If x = 4, then
4*x = 4*4 = 16 = 4 (mod 6)
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If x = 5, then
4*x = 4*5 = 20 = 2 (mod 6)
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If x = 6, then
4*x = 4*6 = 24 = 0 (mod 6)
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The results follow the pattern: 4, 2, 0, 4, 2, 0, 4, 2, 0...
The pattern repeats forever.
The value 3 is not found in that pattern. So there is no possible solution for 4*x = 3 (mod 6)
Answer: No solution
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! a is congruent to b modulo n if n divides a - b
:
in our problem we want to know all the x's such that
:
(4 * x) - 3 is divided by 6
:
1) ((4 * 1) - 3) / 6 = 6 does not divide 1, 1) is not correct answer
2) ((4 * 0) - 3) / 6 = 6 does not divide -3, 2) is not correct answer
3) ((4 * 2) - 3) / 6 = 6 does not divide 5. 3) is not correct answer
:
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4) no solution is the correct answer
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