Edit: Removed solved in title, because I realize I need someone to check my work.Ok, so the problem is a lot more straight forward than I originally approached it (which was a false statement -- so it was excluded).Let R,S, x ∈ N with x ≤ R*S and 0 0 &lt; R ≤ S. Next, define B as a multiplicative factor of x - c with c ≥ 0 0 and B ≤ S such that x − c B = A ≤ R and A ∈ N. What value of B maximizes A?

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Edit: Removed solved in title, because I realize I need someone to check my work.Ok, so the problem is a lot more straight forward than I originally approached it (which was a false statement -- so it was excluded).Let R,S, x   ∈ N with x   ≤ R*S and 0   0  &amp;lt; R   ≤ S. Next, define B as a multiplicative factor of x - c with c   ≥  0 0 and B   ≤ S such that             x      −      c        B    =  A  ≤  R and A   ∈ N. What value of B maximizes A?

Trey Ross · Accepted Answer

Consider the expression       x    B  . For B to be a multiplicative factor of x - c, c must equal the remainder between B and x. Therefore, we can rewrite c as c = x - dB, where d is the unique natural number satisfying both dB   ≤ x and (d + 1)B   &amp;gt; x. Substituting,A =             x      −      (      x      −      d      B      )        B   = d.However, d depends on B, so find   B  ∈  N with   B  ≤ S such that       d    B    ≤  R and       d          B      −      1        &amp;gt;  R. Following these two sets of inequalities will maximize A.

Edit: Removed solved in title, because I realize I need someone to check my work. Ok, so the probl

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