Two Easy Tasks

March 3, 2020

Many of the tasks I publish on this blog come from beginning-programmer forums. Here is a task taken from some sort of entrance examination:

Jason rings every multiple of 13 less than 500. He then crosses every multiple of 17 less than 500. How many numbers get both ringed and crossed?

The test is a multiple-choice examination with possible selections 10, 0, 1 and 4. The solution sheet shows the correct answer is 4. The questioner who posted this question was asking how to calculate the answer given on the solution sheet.

And here is another simple task:

Given positive integer n < 1018, find the sum of the integers from 1 to n, mod 109 + 7. Assume you are using a language that provides 64-bit arithmetic, so no intermediate results can be larger than 264.

Your task is to write a program to solve these two tasks. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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