Find the number of non-negative integral values of x that satisfy the following equation, where $\lfloor \mathrm{x}\rfloor$ denotes the greatest integer less than or equal to x.

$⌊\frac{\mathrm{x}}{9}⌋=⌊\frac{{\mathrm{x}}^2}{99}⌋$

If $\lfloor \mathrm{x}\rfloor$ denotes the greatest integer less than or equal to x, which one of the following could be a suitable value of x for which each term of the following expression is expressed in its simplest form?

$\frac{⌊\mathrm{x}⌋+3}{4},\frac{⌊\mathrm{x}⌋+8}{5},\frac{⌊\mathrm{x}⌋+15}{6},\frac{\lfloor \mathrm{x}\rfloor +24}{7},\dots .\frac{\lfloor \mathrm{x}\rfloor +168}{15},\frac{\lfloor \mathrm{x}\rfloor +195}{16}$

Which of the following are the factors of $2^{387}+3^{344}$?

(i) $216$            (ii) $643$

(iii) $735$          (iv) $7073$