Question 1207685: The inverse of $a$ modulo $44$ is $b$. What is the inverse of $9$ modulo $10$?
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
The inverse of a modulo 44 is b. What is the inverse of 9 modulo 10?
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Inverse of 9 modulo 10 is an integer number 1 <= n <= 9 such that the product
n*9 is equal to 1 modulo 10.
As soon as you pronounce these words mentally (as the definition), the answer just should be in your mind:
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| the inverse of 9 modulo 10 is the number 9 modulo 10. |
+-----------------------------------------------------------+
Indeed, 9*9 = 81, which is equal to 1 modulo 10.
ANSWER. The inverse of 9 modulo 10 is the number 9 modulo 10.
Solved.
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This problem consists of two statements.
Of these two statements, the first one does not bring any relevant information;
therefore, having sanity in the skull, we should ignore this first statement
(by pointing that it is non-sensical).
The second statement brings the question and makes sense (even if consider it
independently of the first statement).
So, I ignore first statement (as if it is empty and as if it does not exist)
and react to the second statement - it is precisely what I do.
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In this problem formulation, the first statement
does not carry any information, is not necessary
and interferes with understanding the rest of the task.
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