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Question 1205221: If a ≡ -25 (mod 7) then a is equal to
Found 4 solutions by MathLover1, math_tutor2020, ikleyn, greenestamps:
Answer by MathLover1(20850)   (Show Source):
Answer by math_tutor2020(3821)  (Show Source):
You can put this solution on YOUR website!
The closest multiple of 7 to 25 is 28
Add it to -25 to get 28+(-25) = 28-25 = 3
Therefore 3 = -25 (mod 7)
Both 3 and -25 give the same remainder when dividing over 7.
Answer by ikleyn(52946)  (Show Source):
You can put this solution on YOUR website! .
If a ≡ -25 (mod 7) then a is equal to
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The question is posed FATALLY INCORRECTLY,
showing that the "composer" does not understand the meaning of words.
If a ≡ -25 (mod 7), then we CAN NOT say to which number "a" is equal to.
We only can say that
a ≡ -25 (mod 7)
is the same class of integer numbers as
a ≡ 3 (mod 7) .
In other words, we only can say that if a ≡ -25 (mod 7), then "a" has the remainder 3 when is divided by 7.
Fixed, solved, answered in a right way and fully explained.
Answer by greenestamps(13219)  (Show Source):
You can put this solution on YOUR website!
As the problem is presented, there is no way to know what a is equal to. By the definition of mod, a can be any number that differs from -25 by an integer multiple of 7.
The usual intent of a problem like this is to have the answer equal to a non-negative number less than 7.
So a typical correct presentation of the problem, allowing a single answer, would be something like this:
"Solve: a ≡ -25 (mod 7) (0 <= a < 7)"
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