Learn Hardcore French: Je n’ai aucun reçu, alors je ne peux pas prouver l’achat. - I have no receipt, so I cannot prove the purchase.

No. In French, negation is typically formed with ne plus a negative word. Aucun(e) means "no/none" and combines with ne: Je n’ai aucun reçu = "I have no receipt(s)." It’s a single logical negation, not like English "I don’t have no...".

Why is "aucun" singular when "receipts" can be plural?

Because aucun is grammatically singular and agrees with the noun’s gender: aucun reçu (masc. sg.), aucune facture (fem. sg.). It means "not a single." If you want a more neutral "no receipts," you can say Je n’ai pas de reçus.

Can I say "Je n’ai pas de reçu" or "Je n’ai pas de reçus"? Which sounds more natural?

Both are correct.

Je n’ai pas de reçu: "I don’t have a receipt" (often implies the one you’d normally expect).
Je n’ai pas de reçus: "I don’t have any receipts" (plural). In everyday speech, these are slightly more common than aucun reçu, which is a bit stronger/more formal.

Does "aucun" change with gender/number?

Yes. Masculine singular aucun, feminine singular aucune. Rare plural forms aucuns/aucunes exist mainly with nouns that are normally plural (e.g., aucuns frais "no fees/expenses"). Otherwise, use the singular.

Is "reçu" here the noun "receipt" or the past participle of "recevoir"?

It’s the noun meaning "a receipt." The spelling is the same as the past participle (reçu) and includes a cedilla. Compare:

Noun: un reçu
Past participle: j’ai reçu = "I received"

Would "ticket de caisse" or "facture" be better than "reçu"?

Depends on context:

un ticket de caisse: cash register receipt from a store/supermarket.
un reçu: generic "receipt" (any proof of payment).
une facture: invoice/bill (often itemized; businesses, utilities, services). For "proof of purchase," any of these might serve, but the document type can matter.

Why use "alors" here? Could I use "donc" or "du coup"?

Yes:

alors = "so/then," common and neutral-conversational.
donc = "so/therefore," a bit more logical/concise; slightly more formal in writing.
du coup = very colloquial "so/as a result."
par conséquent = formal "therefore." All would fit, with register differences.

Where does the negation go with a modal plus infinitive? Why "je ne peux pas prouver"?

Place ne ... pas around the conjugated verb (peux) and keep the infinitive (prouver) after it: je ne peux pas prouver. If you say je peux ne pas prouver, the negation applies to the infinitive and means "I can/I'm allowed to not prove," which is a different meaning.

Can I drop "ne" in speech?

In casual speech, many drop ne: J’ai pas de reçu. However, with aucun, standard French keeps ne; J’ai aucun reçu is perceived as nonstandard. If you’re speaking informally, prefer J’ai pas de reçu rather than dropping ne with aucun.

Why "l’achat"? Could I say "mon achat" or something else?

L’achat uses the definite article because both speakers know which purchase is meant (the one under discussion). Alternatives:

mon achat = my purchase (emphasizes ownership).
cet achat = this purchase (deictic).
prouver que je l’ai acheté = "prove that I bought it."
With a complement: prouver l’achat de ce produit.

Is there a more idiomatic way to say "proof of purchase"?

Yes: une preuve d’achat or un justificatif d’achat. You could say:

Je n’ai aucune preuve d’achat.
Je n’ai pas de preuve d’achat. These are very common in customer-service contexts.

If I replace "l’achat" with a pronoun, where does it go?

Use the direct object pronoun le and place it before the infinitive: Je ne peux pas le prouver. Negation still wraps the conjugated verb: ne ... pas around peux.

Is "Je ne peux prouver l’achat" (without "pas") correct?

Not in modern standard French. You need ne ... pas: Je ne peux pas... A very formal/literary alternative is Je ne puis prouver l’achat (using puis, the old present of pouvoir), but that’s rare today.

Any pronunciation tips for the sentence?

Je n’ai: [ʒə n‿e] (the schwa in je can drop: [ʒ n‿e]).
aucun: [okœ̃] (nasal vowel).
reçu: [ʁ(ə)sy] (the middle schwa may be faint or dropped in rapid speech).
alors: [alɔʁ].
je ne peux pas: [ʒ(ə) nə pø pa] (often [ʒ pø pa] in casual speech).
prouver: [pʁuve].
l’achat: [laʃa]. Linking and elisions: n’ in n’ai, l’ in l’achat.

Is the comma before "alors" necessary?

Optional. A comma can mark the pause: ..., alors ... In short sentences it’s often omitted; in writing, both with and without the comma are acceptable.

How would I say "none of the receipts"?

Use aucun(e) de + definite article: Je n’ai conservé aucun des reçus = "I kept none of the receipts." This refers to a specific known set, unlike aucun reçu which is general.