The least positive value of x such that 98 - x -4 5 isA- 4B- 5C- 1D- 2

The correct option is A 498 ≡ nbsp;(x + 4)(mod 5) ⇒ 98 (x + 4) = 5n, for some integer n. ⇒ 94 x nbsp; = 5n i.e., 94 x is a multiple of 5. ∴The lea ...

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Byju's Answer

Standard X

Mathematics

Modular Arithmetic and Congruence Modulo

The least pos...

Question

The least positive value of $x$ such that $98 \equiv (x + 4) (m o d 5)$ is ___.

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Solution

The correct option is A 4
$98 \equiv (x + 4) (m o d 5)$
$\Rightarrow 98 - (x + 4) = 5 n, for some integer n$ .
$\Rightarrow 94 - x = 5 n$
i.e., $94 - x$ is a multiple of 5.
$∴$ The least positive value of $x$ so that $98 \equiv (x + 4) (m o d 5)$ holds must be 4 as 94 - 4 = 90, which is the nearest multiple of 5 less than 94.

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The least positive value of x such that 98≡(x+4)(mod 5) is ___.

The correct option is A 498≡(x+4)(mod 5) ⇒98−(x+4)=5n, for some integer n. ⇒94−x=5n i.e., 94−x is a multiple of 5. ∴The least positive value of x so that 98≡(x+4)(mod 5) holds must be 4 as 94 - 4 = 90, which is the nearest multiple of 5 less than 94.

The least positive value of $x$ such that $98 \equiv (x + 4) (m o d 5)$ is ___.