A research grant requires that a number of distinct positive integers each less than or equal to 50 be selected such that each is congruent to 3 modulo 7. What is the total number of such integers?

Sun, 19 Apr 2026 00:32:19 +0000

**A research grant requires that a number of distinct positive integers each less than or equal to 50 be selected such that each is congruent to 3 modulo 7. What is the total number of such integers?** Across academic circles and innovation hubs, researchers and funders are increasingly focusing on structured data patterns—especially when evaluating eligibility criteria for grants, studies, or selection processes. One recurring mathematical requirement surface frequently: identifying positive integers up to 50 that satisfy a specific congruence condition. A tip often surfacing in data literacy discussions: how many distinct positive numbers less than or equal to 50 fit the pattern “third modulo 7”?
Understanding this reveal offers insight into how numerical logic shapes research design and funding parameters in the U.S. academic and innovation ecosystem. --- ### Why This Pattern Is Gaining Attention in the US