Although many of the clues have multiple answers, there is only one
... eight times in Pascal’s triangle. 24 The maximum number of regions that can be formed by joining 27 points on a circle with straight lines. 27 The number of straight lines that go through at least two points of a 10×10 grid of points. 28 The sum of four consecutive positive cubes. 29 Five less than ...
... eight times in Pascal’s triangle. 24 The maximum number of regions that can be formed by joining 27 points on a circle with straight lines. 27 The number of straight lines that go through at least two points of a 10×10 grid of points. 28 The sum of four consecutive positive cubes. 29 Five less than ...
Some materials for problem-solving sessions — modular
... coordinates. Prove that the side of the cube is of integral length. 39. (a) Is it possible to place an uncountable family of circles in the plane, if no circle is allowed to be placed inside another one? (b) Let us call a T-shaped figure in the plane the union of two perpendicular segments, with an ...
... coordinates. Prove that the side of the cube is of integral length. 39. (a) Is it possible to place an uncountable family of circles in the plane, if no circle is allowed to be placed inside another one? (b) Let us call a T-shaped figure in the plane the union of two perpendicular segments, with an ...
Raji 5.2, Primitive roots for primes: 8. Let r be a primitive root of p
... Which are 2, 4, pe , or 2pe for an odd prime p? Only 4 and 125, right? 2. Find primitive roots of 4, 25, 18. For 4, the primitive root is 3. For 25, I would …rst try 2. The powers of 2 are 2; 4; 8; 16; 7; 14; 3; 6; 12; 24 = 1, so 210 1 and ord25 2 = 20 = ' (25). For 18, the …rst candidate is 5, whos ...
... Which are 2, 4, pe , or 2pe for an odd prime p? Only 4 and 125, right? 2. Find primitive roots of 4, 25, 18. For 4, the primitive root is 3. For 25, I would …rst try 2. The powers of 2 are 2; 4; 8; 16; 7; 14; 3; 6; 12; 24 = 1, so 210 1 and ord25 2 = 20 = ' (25). For 18, the …rst candidate is 5, whos ...
