+0

# gveme

0
175
3
+1167

Find the least positive integer x that satisfies $$x+4609 \equiv 2104 \pmod{12}$$.

tertre  Mar 23, 2017
Sort:

#1
0

The smallest positive integer =3

General formula: 3 + 12n, for n = 0, 1, 2,.....etc.

Guest Mar 23, 2017
#2
+6810
+1

if $$x+4609 \equiv 2104 \pmod{12}$$ , x + 2505 is divisible by 12

x must be an odd number in order to make x + 2505 divisible by 12.

Trial and error:

Try x = 1, 1 + 2505 = 2506 <-- not divisible by 12.

Try x = 3, 3 + 2505 = 2508 <-- divisible by 12(2508 = 2 x 2 x 3 x 11 x 19)

Therefore the least positive integer x is 3.

MaxWong  Mar 23, 2017
#3
+18625
+1

Find the least positive integer x that satisfies

$$x+4609 \equiv 2104 \pmod{12}$$.

$$\begin{array}{|lrcll|} \hline & x+4609 &\equiv& 2104 \pmod{12} \\ & x+4609-2104 &=& n \cdot 12 \quad & | \quad n \in \mathbb{N} \\ & x+2505 &=& n \cdot 12 \\ & x&=& n \cdot 12 -2505 \\\\ \text{so } & n \cdot 12 &=& 2505 \\ & n &=& \uparrow \frac{2505}{12} \uparrow \\ & n &= & \uparrow 208.75 \uparrow \\ & n &= & 209 \\\\ & x&=& 209 \cdot 12 -2505 \\ & x&=& 2508 -2505 \\ & \mathbf{x} & \mathbf{=} & \mathbf{3} \\ \hline \end{array}$$

heureka  Mar 24, 2017

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details