Four bells ring at intervals of 5, 10, 12 and 15 minutes respectively. If they start ringing together at 3 o'clock, after what interval of time will they ring together and how many times will they ring together in 18 hours? If the number A is exactly divisible by 36, then what is the value of A? If the product of two numbers is and their Highest Common Factor is 17, then what is the difference between the two numbers?
What is the Highest Common Factor of How many numbers from 1 to are divisible by 7? What is the LCM of square of 4, cube of 3 plus 1 and the square of 6?. If the product of two numbers is , then what is their Highest Common Factor?
If 'a' and 'b' are two smallest positive prime numbers, then what is the difference between their L. Suggested Test Series. Madhya Pradesh Patwari Suggested Exams.
More Quantitative Aptitude Questions Q1. The average speed of Columbus. Which of the following fractions is the largest? Using the preceding applet to experiment would be tedious. Test out different values of n , and try to determine which values of a will appear for a given value of n. Note: You may find it easier to think of this question in the following equivalent form: for which values of a does the congruence equation ax 1 mod n have solutions? As you can see, the problem of finding an inverse for a modulo n is really a special case of the general problem considered in the Prelab discussion, namely, to solve the linear congruence equation.
This means that I will quickly converge to the inverse. We can start with a very interesting observation: if we use 3-bit words, instead of bit or bit words, then every number is its own inverse. The first call to the recurrence formula gives me 6 bits, then 12 bits for the second call, then 24 bits, then 48 bits, then 96 bits, and so forth. So, we need to call our recurrence formula 4 times for bit values and 5 times for bit values. I could actually go to bit values by calling the recurrence formula 6 times.
I wrote a complete command-line program that can invert any odd number quickly. Each call to the recurrence formula should consume about 5 CPU cycles so that the whole function should take no more than 25 cycles or no more than the cost of a single integer division. Actually, it might be cheaper than a single integer division. Because of the way we construct the inverse, if you somehow knew the bit inverse, you could call the recurrence formula just once to get the bit inverse.
So there is no magic involved. My code seems to assume that I am working with unsigned integers, but the same algorithm works with signed integers, and in binary form, it will provide the same results. Some people point me at On Newton-Raphson iteration for multiplicative inverses modulo prime powers by Dumas Credit : Marc Reynolds asked on Twitter for an informal reference on computing the multiplicative inverse modulo a power of two. It motivated me to write this blog post.
He finally wrote a decent article on the subject with many interesting remarks. View all posts by Daniel Lemire. Interesting article!
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