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how many faces of rubik's cube can be simultaneously solved ??? ...
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Show that a4b+1 - a is divisible by 30 ...
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1. Give the continued fractions expansions of a = d2±1 , d element of Z 2. Determine the least positive solution of x2 − ny2 = 1, where n = d2 + 2 ...
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given that a2 + b2+ c2 = 8 prove that a3 + b3 + c 3 ≥ 16 2/3 . ...
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FIND ALL THE INTEGRAL TRIANGLES WHOSE PERIMETER EQUALS THERE AREA . ...
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Find all natural numbers n > 1 such that n2 does not divide (n − 2)!. ...
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1) Every living person has shaken hands with a certain number of other persons . prove that the count of the number of the people who have shaken hands an odd number of time must yield an even number. 2) In a chess is it poss ...
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1>how many odered pairs of (m,n) of positive integer are solution to 4/m + 2/n = 1 ? 2>prove that if a +b + c =0 then a3+b3+c3 = 3abc ...
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SHOW THAT a12- b12 IS DIVISIBLE BY 91 ,IF a AND b ARE BOTH PRIME TO 91 ...
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post different methods to find if 22051946 is a perfect square . at least 5 shorter methods ...
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prove that 32n+7 is a multiple of 8 ...
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A boy pushes a cylinder of mass m1 with a help of a plank of mass m2 as shown in the figure .There is no slipping at any contact. The horizontal component of force applied by the man is F . Find a) Acceleration of the plank a ...
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Suppose positive integers m, n, K satisfy mn = K2 + K + 3. Prove that at least one of the following Diophantine equations x2+11y2=4m and x2+11y2=4n has a solution (x, y) with x, y being odd numbers EDITED sorry for the incorr ...
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1) You've got 27 coin, each of them is 10 g, except for 1. The 1 different coin is 9 g or 11 g (heavier, or lighter by 1 g). You should use balance scale that compares what's in the two pans. You can get the answer by just co ...
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1) There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to wh ...
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You are on a trip to a tropical island. As you find out, the island is inhabited by three tribes. As it turns out, you arrive right when the chiefs of these tribes are all meeting. One chief is wearing a blue headress, one is ...
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if p is a prime no. show that (p-2r) ! (2r-1) ! - 1 is divisible by p. ...
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if n is number greater than 3, show that n2-1 is a multiple of 24. ...
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