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Number Theory
Divisibility
If the number \(\overline{7448x24y}\) is divisible by \(72\), and \(x \ne y,\) find \(x-y\).
by
Azhaghu Roopesh M
\[ {\huge \color{blue}N = \color{green} {123,4}\color{red}{F}\color{green}{6,789}}\]
If \(\color{red} {F}\) is replaced with a digit from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) at random, what is the probability that \(\color{blue} {N}\) will be divisible by 3?
by
Chung Kevin
For similar problems, you can read my note on Construction.
by
Calvin Lin
As \(n\) ranges over all real values in the interval \( [0, 100] \), how many values of \(n\) are there such that \( 4n+ 1 \) is an odd integer?
by
Arron Kau
\[ \begin{array} { l l l l } & && & A & A & A \\ \times & & & & A & A & A \\ \hline &A & A & 8 & 0 & 0 & 1\\ \end{array} \]
What is the three digit number \(\overline{AAA}?\)
by
Mohd Sasa