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I've started this topic in the algebra page already and want more answers so am spreading it fast
1. A convex polygon has 80 sides. Inside the polygon 50 points are taken, in such a way that no 3 points are collinear. I tis cut into triangles, such that the vertices of the triangle are just the 80 vertices of the polygon and the 50 points within it.
2.In a class, there were 10 students. Each student is asked to write the sum of the ages of the nine other students, giving 9 unique sums:
82,83,84,86,87,88,90,91 and 92
The 10th sum is equal to one of the other sums. Find the ages of the students.
3. Find the remainder of 2^1990 divided by 1990.
4.Find the remainder when 3^333 is divided by 14.
5. Prove a^n + b^n =c^n is not possible for n>2.
Note: I know the answer to 4 of these problems and not the other, but please show me the procedure to do these sums. ( I know that no one can do all of them)
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