Loaded dice with a uniformly distributed sum

Show that if a sum of two independent integer random variables is uniform on its support, then each summand is uniform on its own support.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"probability",
5	"algebra"
6	],
7	"type": "construction",
8	"also": [
9	"proof"
10	],
11	"source": {
12	"key": "green-100",
13	"name": "Ben Green's 100 open problems",
14	"url": "https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.28",
15	"id": "28",
16	"curator": "Ben Green",
17	"poser": "Emmanuel Amiot",
18	"status": "open",
19	"as_of": "2026-10-20",
20	"catalog": "0521c19bbd38"
21	},
22	"review": true,
23	"approval": "first-time"
24	}