Question 10
How many distinct integers are there among the following numbers?
$$\left\lfloor\frac{1^2+1}{100}\right\rfloor,\left\lfloor\frac{2^2+2}{100}\right\rfloor,\left\lfloor\frac{3^2+3}{100}\right\rfloor,\ldots,$$
$$\left\lfloor\frac{100^2+100}{100}\right\rfloor.$$
Here $\lfloor a\rfloor$ denotes the greatest integer less than or equal to $a$.
$$\left\lfloor\frac{1^2+1}{100}\right\rfloor,\left\lfloor\frac{2^2+2}{100}\right\rfloor,\left\lfloor\frac{3^2+3}{100}\right\rfloor,\ldots,$$
$$\left\lfloor\frac{100^2+100}{100}\right\rfloor.$$
Here $\lfloor a\rfloor$ denotes the greatest integer less than or equal to $a$.