Chittur Gopalakrishnavishwanathasrinivasaiyer Lemma

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We know that an $x$ exists that equal to $42\, \cdot$ $\text{mod} \sqrt{4761}.$ This $x$ is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at $(x^n, n^x)$ where $n$ is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the $n$th root unity is the same thing as $x^n$ $\text{mod}$ $(42*10\cdot(70-1)^n).$ Finally, you'll se it in combo! The number ways you can shuffle $n$ things into $n^2 + nk + 1$ items where $k$ is the number of partitions in an item is the $x^{23\cdot3}.$ My coaches Iyer Sir and Barnes approved this nice lemma.