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The remainder when the square of any pri...

The remainder when the square of any prime number greater than `3` is divided by `6` is

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The set of intergers can be classified into k classes, according to the remainder obtained when they are divided by K (where is a fixed natural number). The classification enables is solving even some more difficult problems of number theory e.g. (i) even, odd classification is based on whether ramainder is 0 or 1 when divided by 2. (ii) when divided by 3, the ramainder may be 0,1,2. Thus, there are three classes. The number obtained, when the square of an integer is divided by 3, is

RD SHARMA ENGLISH-REAL NUMBERS-All Questions
  1. Show that one and only one out of n ,n+2 or n+4 is divisible by 3, whe...

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  2. Prove that n^2-n divisible by 2 for every positive integer n.

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  3. The remainder when the square of any prime number greater than 3 is ...

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  4. Use Euclid’s division algorithm to find the HCF of 4052 and 12576.

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  5. Use Euclid’s division algorithm to find the HCF of 210 and 55.

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  6. If n is a natural number, then 9^(2n)-4^(2n) is always divisible by (a...

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  7. What can you say about the prime factorisations of the denominators of...

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  8. If p1a n dp2 are two odd prime numbers such that p1> p2, then p1 2-p2 ...

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  9. There is a circular path around a sports field. Priya takes 18 minutes...

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  10. A rectangular courtyard is 18m 72cm long and 13m 20cm broad. It is to ...

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  11. If the prime factorization of a natural number n is 2^3*3^2*5^2*6, wri...

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  12. A circular field has a circumference of 360km. Three cyclists start ...

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  13. In a morning walk three persons step off together, their steps measure...

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  14. Prove that sqrt(2)+sqrt(5) is irrational.

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  15. Show that there is no positive integer n for which sqrt(n-1)+sqrt(n+1...

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  16. A merchant has 120 litres of oil of one kind, 180 litres of another ...

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  17. Two brands of chocolates are available in packs of 24 and 15 respec...

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  18. What is the largest number that divides 626, 3127 and 15628 and lea...

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