MathDB

3

Part of 2013 Danube Mathematical Competition

Problems(2)

diophantine 85^m-n^4=4

Source: Danube 2013 junior p3

7/22/2019
Determine the natural numbers m,nm,n such as 85m−n4=485^m-n^4=4
Diophantine equationdiophantineExponential equationexponentialnumber theory
r-chromatic simple graph with no cycle of < =6 edges

Source: Danube 2013 p3

7/22/2019
Show that, for every integer r≥2r \ge 2, there exists an rr-chromatic simple graph (no loops, nor multiple edges) which has no cycle of less than 66 edges
graph theorygraphgraph cyclescombinatorics