Let . Then the number of elements in the set is .

Question

Let . Then the number of elements in the set  is .

Canvas Classes · Accepted Answer

🧠 The LHS Looks Like Reverse  Expansion

Read the equation: . Expand the LHS:

.

Move terms: .

Divide both sides by :

.

But the LHS is exactly . So

.

That single identity collapses the whole equation. Now count solutions in .

🗺️ Working It Out

gives  for integer .

Let , so  — specifically  rad (about ).

.

Count  in .

For : . So  must lie in , i.e. . So .

That gives 5 candidate  values:

- :  ✓ (in )
- :  ✓
- :  ✓
- :  ✓
- :  ✓ (just under )

Check none coincide with excluded valu

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