Go green, plant trees

Number Theory Level 4

In a school's \(\color{Green}{\textbf{Go Green movement}}\) , they planned to take a tree-plantation event.

They have " \(\color{Purple}{k}\) " \(\color{Green}{\text{plants}}\) for planting. The \(\color{Red}{\text{math teacher}}\) of the school tells that if they decide to plant them in '\(x\)' rows, then '\(y\)' \(\color{Green}{\text{plants}}\) remain. The following table shows the values of \(x\) and \(y\) as seen by the teacher.

\[\color{Blue}{ \begin{array}{|c||c|} x & y \\ \hline 17&3\\ 19&4\\ 23&7\\ 29&12\\ \end{array} }\]

Teacher asks the students to find the number of plants, i.e. \(\color{Purple}{k}\)

Can you help the students by telling what is the \(\color{Blue}{\text{positive integer}}\) \(\color{Purple}{k}\), if it is the smallest to satisfy the above property ?

Most probably, after you get the answer, you'll say "It's indeed a huge movement to 'Go green', so many plants ! "


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