### Questions (62)

 46 Are rational points dense on every circle in the coordinate plane? 10 How do you know if a line is straight? 5 The gambler makes 100 bets and wins 10. How much money does he have at the end? 4 Finding the formula of the sum $\frac1{1\cdot2} + \frac1{2\cdot3}+ \frac1{3\cdot4} + \cdots + \frac1{n\cdot(n+1)}$? [duplicate] 3 Periodic or non periodic function plotting

### Reputation (279)

This user has no recent positive reputation changes

### Answers (3)

 1 Prove that for integers $a,b$, if $3|ab$ with $15x+by = 1$ for some integers $x,y$ then $3|a.$ 0 Kepler's books: Mysterium Cosmographicum, Astronomia Nova, and Harmonices Mundi -1 There exists an integer k such that $n = 3k+1$. Then $n^2 = (3k+1)^2 =9k^2 + 6k + 1 = 3 (3k2 +2k)+1$.

### Tags (56)

 1 divisibility × 3 0 calculus × 6 1 proof-writing × 2 0 probability × 5 0 number-theory × 12 0 modular-arithmetic × 5 0 linear-algebra × 8 0 geometry × 4 0 graph-theory × 7 0 integration × 4

### Accounts (15)

 Mathematics 279 rep 625 Philosophy 156 rep 6 Mathematics Educators 143 rep 4 Meta Stack Exchange 141 rep 4 Earth Science 121 rep 1

### Badges (22)

 Nice Question × 2 Good Question Cleanup Excavator Popular Question × 6 Organizer Yearling × 2 Benefactor Notable Question × 3 Tumbleweed

### Active bounties (0)

This user has no active bounties

### Votes cast (200)

all time   by type
198 up 66 question
2 down 134 answer