The number of solutions of the equation is:

Question

The number of solutions of the equation  is:

Canvas Classes · Accepted Answer

🧠 Bound Both Sides — LHS , RHS

Read the equation: . Look at the two sides separately:

- LHS: , with equality iff .
- RHS: , with equality iff , i.e. .

For the equation to hold, both sides must equal  simultaneously:

-  for some integer .
- , i.e. .

Both conditions:  is a special case of  (when ). So the combined condition is .

Count  in  — that means , i.e. , so : 5 values.

🗺️ Working It Out

The two bounds force equality:

LHS : equality requires .

RHS : equality requires .

Both hol

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